Understand basic geometric terms: point, line, ray, and line segment
Identify types of lines: parallel, intersecting, and perpendicular
Understand what an angle is and identify its parts (arms and vertex)
Classify angles: acute, right, obtuse, straight, reflex, and complete angle
Measure angles using a protractor (inner and outer scale)
Draw angles of given measures using a protractor
Identify angles in real-life objects and situations
Calculate angles formed by clock hands at different times
Introduction — Angles Are Everywhere!
Look around you — angles are everywhere! When you open a book, the two covers form an angle. When a cricket batsman lifts his bat to hit a six, the bat makes an angle with the ground. The hands of a clock form different angles as time passes. The corners of your classroom, the slopes of rooftops, the opening of scissors, the blades of a fan — all involve angles.
In India, you can see beautiful angles in architecture — the pointed arches of Mughal monuments like the Taj Mahal, the geometric patterns in Rangoli designs, and the sloping roofs of houses in hilly areas like Shimla and Manali. Even the angle at which ISRO launches rockets matters for reaching the correct orbit!
In this chapter, we will learn about points, lines, rays, and line segments. Then we will explore types of lines and dive deep into angles — what they are, how to measure them, how to draw them, and how to find them in the world around us.
Basic Geometric Terms
Before we learn about angles, let us understand the building blocks of geometry:
1. Point
A point is an exact location in space. It has no length, no width, and no height — it is just a position. We represent a point with a dot (.) and name it with a capital letter.
Example: Point A is written as A and shown as a dot: • A Real-life examples: The tip of a pencil, a star in the night sky (from far away), a pinhole on paper.
2. Line
A line is a straight path that extends endlessly in both directions. It has no starting point and no ending point. We show this with arrows on both ends. A line has infinite length but no thickness.
A line passing through points A and B is written as: ↔AB (with a double-headed arrow symbol above AB).
Example: ←——————→ (arrows on both ends)
A B Real-life: Imagine railway tracks going on forever in both directions — that is like a line (though real tracks do end!).
3. Ray
A ray starts at one point and goes on forever in one direction. It has one endpoint (starting point) and one arrow. Think of a ray of sunlight — it starts from the Sun and travels endlessly into space.
A ray starting from point A and passing through B is written as: →AB (with a single arrow above, pointing from A to B).
Example: A ——————→ (one fixed point, one arrow) Real-life: A torch beam, a laser pointer, sunlight from the Sun.
4. Line Segment
A line segment is a part of a line that has two definite endpoints. It has a fixed, measurable length. We can measure a line segment using a ruler.
A line segment with endpoints A and B is written as: AB (with a bar above it) or simply seg AB.
Example: A ——————— B (two fixed endpoints, no arrows) Real-life: The edge of your notebook, a pencil, the side of a door, a cricket pitch (22 yards).
Image needed: A comparison diagram showing all four basic geometric terms side by side: (1) Point — a dot labelled A, (2) Line — extending with arrows both sides through A and B, (3) Ray — starting at A with arrow through B, (4) Line Segment — from A to B with endpoints marked. Each clearly labelled with its name and key property (e.g., "no length" for point, "infinite length" for line, etc.). Style: Clean educational diagram, colourful labels, child-friendly, white background Size: 750×400px
Comparison Table
Term
Endpoints
Length
Symbol/Representation
Example
Point
It IS a point
No length
• A
Tip of needle
Line
No endpoints (arrows both sides)
Infinite (goes on forever)
↔AB
Horizon line
Ray
One endpoint (one arrow)
Infinite in one direction
→AB
Torch beam
Line Segment
Two endpoints
Fixed, measurable
AB (with bar)
Edge of ruler
Think About It: Can you measure a line? No! A line goes on forever, so it has no fixed length. But a line segment has two endpoints, so we CAN measure it. That is why we use a ruler to measure line segments, not lines.
Types of Lines
When two or more lines exist together on a surface, they can relate to each other in different ways:
1. Parallel Lines
Parallel lines are lines that are always the same distance apart. They never meet, no matter how far you extend them in either direction. We use the symbol ∥ to show parallel lines. If line AB is parallel to line CD, we write: AB ∥ CD.
Real-life examples of parallel lines:
Railway tracks
Two opposite edges of your notebook
The horizontal lines on ruled paper
Two opposite sides of a rectangular door
Lanes on a highway
The two rails of a ladder
2. Intersecting Lines
Intersecting lines are lines that cross each other at exactly one point. This point where they meet is called the point of intersection. When two lines intersect, they form angles at the point of intersection.
Real-life examples of intersecting lines:
Two roads crossing at a traffic signal
The letter X
Scissors when open (the two blades)
The crossroads in your neighbourhood
The hands of a clock (they meet at the centre)
3. Perpendicular Lines
Perpendicular lines are a special type of intersecting lines. They intersect at exactly 90° (a right angle). We use the symbol ⊥ to show perpendicular lines. If line AB is perpendicular to line CD, we write: AB ⊥ CD.
Real-life examples of perpendicular lines:
The corner where two walls meet
The letter L and the letter T
The edges of a book where the spine meets the top
The plus sign (+)
A vertical pole on flat ground
The red cross symbol on a hospital
Image needed: Three diagrams side by side: (1) Parallel lines — two lines with arrows, same distance apart, with the ∥ symbol and real-life example (railway tracks); (2) Intersecting lines — two lines crossing at a point, point of intersection marked; (3) Perpendicular lines — two lines crossing at 90° with a small square at the corner. Each labelled clearly. Style: Clean flat diagram, colour-coded (blue for parallel, green for intersecting, red for perpendicular), child-friendly Size: 800×350px
Type
Definition
Symbol
Key Feature
Parallel Lines
Lines that never meet
∥
Always same distance apart
Intersecting Lines
Lines that cross at one point
—
Form angles at the point of intersection
Perpendicular Lines
Lines that meet at 90°
⊥
Form right angles (marked with a small square)
Think About It: Are all perpendicular lines also intersecting lines? YES! Perpendicular lines are a special case of intersecting lines — they intersect at exactly 90°. But not all intersecting lines are perpendicular — most intersecting lines meet at angles other than 90°.
What is an Angle?
An angle is formed when two rays share a common starting point. The common starting point is called the vertex, and the two rays are called the arms of the angle.
Parts of an Angle
Vertex: The common endpoint where the two rays meet (the corner point)
Arms: The two rays that form the angle
Interior: The space between the two arms (inside the angle)
We use the symbol ∠ (angle symbol) to denote an angle. An angle at vertex B with arms BA and BC is written as ∠ABC or ∠CBA (the vertex letter is always in the middle). If there is only one angle at a vertex, we can simply write ∠B.
Example: Open a pair of scissors. The point where the two blades are joined is the vertex. The two blades are the arms. As you open the scissors wider, the angle between the blades increases!
How is an Angle Measured?
Angles are measured in degrees, using the symbol ° (a small circle above and to the right). One complete rotation (full circle) = 360°. A half rotation (straight line) = 180°. A quarter rotation (right angle) = 90°.
Understanding degrees:
Imagine standing and facing North. If you turn all the way around back to North = 360° (full turn)
If you turn to face South (opposite direction) = 180° (half turn)
If you turn to face East (quarter turn to the right) = 90° (quarter turn)
Types of Angles
Angles are classified based on their measure (how many degrees they are). There are six types of angles:
Type of Angle
Measure
What It Looks Like
Real-Life Example
Acute Angle
Greater than 0° but less than 90°
A narrow opening, less than a right angle
Hands of a clock at 1:00 (30°), a slice of pizza, tip of a pencil
Right Angle
Exactly 90°
A perfect L-shape, marked with a small square (□)
Corner of a book, corner of a room, the letter L, clock at 3:00
Obtuse Angle
Greater than 90° but less than 180°
A wide opening, more than a right angle
An open book (partially), hands of clock at 4:00 (120°), reclining chair
Straight Angle
Exactly 180°
A straight line (the two arms form a line)
A ruler lying flat, hands of clock at 6:00, a fully stretched arm
Reflex Angle
Greater than 180° but less than 360°
More than a straight line — goes past the straight angle
The larger angle when clock shows 10:00, a door opened more than halfway around
Complete Angle (Full Angle)
Exactly 360°
A full rotation — both arms overlap after going all the way around
A spinning top completing one full turn, the minute hand going around once
Image needed: Six angle diagrams arranged in a grid (2×3 or 3×2), each showing: (1) Acute angle — labelled with "Less than 90°", (2) Right angle — with the small square symbol, labelled "Exactly 90°", (3) Obtuse angle — labelled "Between 90° and 180°", (4) Straight angle — labelled "Exactly 180°", (5) Reflex angle — labelled "Between 180° and 360°", (6) Complete angle — labelled "Exactly 360°". Each with a different colour and clear arc marking the angle. Style: Clean educational diagram, colour-coded angles with arc markers, child-friendly Size: 800×500px
Quick Way to Remember
Acute = "a-cute" little angle (small, less than 90°)
Right = exactly 90° (perfectly upright, like an "L")
Obtuse = "obese/fat" angle (wide, between 90° and 180°)
Straight = 180° (forms a straight line)
Reflex = "reflects back" past 180° (more than a straight angle)
Complete = 360° (comes all the way back to the start)
Examples of specific angles and their types:
Angle Measure
Type
45°
Acute angle
90°
Right angle
120°
Obtuse angle
180°
Straight angle
250°
Reflex angle
360°
Complete angle
15°
Acute angle
179°
Obtuse angle
181°
Reflex angle
89°
Acute angle
Measuring Angles with a Protractor
A protractor is a tool shaped like a half-circle (semi-circle). It has markings from 0° to 180° and is used to measure and draw angles. A protractor has two scales — an inner scale and an outer scale — that read in opposite directions.
Parts of a Protractor
Baseline: The straight edge at the bottom (0° line)
Centre point: The small mark or hole at the middle of the baseline
Inner scale: Reads from 0° on the right to 180° on the left
Outer scale: Reads from 0° on the left to 180° on the right
Steps to Measure an Angle
Step 1: Place the protractor so that the centre point is exactly on the vertex of the angle.
Step 2: Align the baseline of the protractor along one arm of the angle. Make sure the arm passes through the 0° mark.
Step 3: Look at where the other arm of the angle crosses the scale on the protractor.
Step 4: Read the degree marking where the second arm crosses. Important: Use the scale that starts from 0° on the arm you aligned!
How to choose the correct scale:
- If the first arm is on the right side (pointing right), use the inner scale (which starts at 0° on the right).
- If the first arm is on the left side (pointing left), use the outer scale (which starts at 0° on the left).
Tip: Always check if your answer makes sense! If the angle looks less than 90° (acute), your reading should be less than 90°. If it looks wider than 90° (obtuse), your reading should be more than 90°.
Image needed: A step-by-step visual guide showing how to measure an angle with a protractor. Show a protractor placed on an angle with: (1) centre point on vertex (labelled), (2) baseline along one arm (labelled), (3) arrow pointing to where the other arm crosses the scale (labelled with the degree reading). Include labels for inner scale and outer scale. Show the angle being measured as approximately 60°. Style: Clean educational diagram, labelled arrows, colour highlighting on key parts, child-friendly Size: 700×450px
Practice Reading:
Meera measured an angle and the other arm crossed at the 50° mark on one scale and 130° on the other scale. The angle looked smaller than a right angle. Which reading is correct?
Answer: Since the angle looks less than 90° (acute), the correct reading is 50°. The 130° reading is from the wrong scale.
Drawing Angles with a Protractor
You can also use a protractor to draw an angle of any given measure. Follow these steps:
Steps to Draw an Angle (e.g., Draw ∠ABC = 75°):
Step 1: Draw a ray BC using a ruler. This will be one arm of the angle. Mark point B (this will be the vertex).
Step 2: Place the protractor with the centre point on B (the vertex) and the baseline along ray BC.
Step 3: Starting from 0° on the scale (from the side where ray BC points), count up to 75°. Mark a small dot at 75°. Call this point A.
Step 4: Remove the protractor. Using a ruler, draw a ray from B through point A.
Step 5: Label the angle as ∠ABC = 75°. Draw a small arc between the arms to show the angle.
Example 2: Draw an angle of 135°
Since 135° is an obtuse angle (greater than 90°), make sure you read past the 90° mark on your protractor. Follow the same steps — draw a ray, place protractor, mark at 135°, draw the second ray. The opening will be wider than a right angle.
Think About It: Can you draw a reflex angle (say 270°) directly with a normal protractor? No! A protractor only goes up to 180°. To draw 270°, you would draw 360° − 270° = 90° and mark the reflex (larger) side. Or draw the angle going the other way.
Angles in Real Life
Angles are not just in textbooks — they are part of everyday life! Let us explore some real-life examples:
Angles in Indian Architecture
Pointed arches in Mughal buildings (Taj Mahal, Red Fort) — the top of the arch forms an acute angle
Dome shapes — the curve of a dome creates obtuse angles at different points
Temple gopurams — the sloping sides form angles with the ground
Rangoli patterns — use precise angles (60°, 90°, 120°) to create symmetrical designs
Sloping roofs in hill stations — form acute angles with the horizontal to let rain and snow slide off
Angles in Sports
Cricket: A batsman's bat makes different angles with the ground for different shots. A straight drive ≈ 90° with the ground. A cover drive ≈ 45°.
Football: The angle of a penalty kick determines where the ball goes
Badminton: The angle of the racket decides whether the shuttle goes up or down
Archery: Arrows are launched at specific angles to reach the target
Angles in Everyday Objects
Object / Situation
Approximate Angle
Type
Corner of a notebook
90°
Right angle
Hands of scissors when slightly open
20°–30°
Acute angle
A door opened halfway
90°
Right angle
A door fully open (flat against wall)
180°
Straight angle
Slice of pizza (standard 8-slice)
45°
Acute angle
A reclining chair (leaned back)
120°–150°
Obtuse angle
Hands of a clock at 3:00
90°
Right angle
Hands of a clock at 6:00
180°
Straight angle
A fan blade from the next blade
120° (3 blades) or 90° (4 blades)
Obtuse / Right
Angles on a Clock Face
A clock face is a circle (360°). The 12 numbers divide it into 12 equal parts. So the angle between any two consecutive numbers on a clock is:
Clock Angle Formula
Total degrees in a circle = 360°
Number of hour divisions = 12
Angle between two consecutive numbers = 360° ÷ 12 = 30°
Angle between hour and minute hand = Number of hour gaps × 30°
Examples of angles at exact hours (minute hand on 12):
Time
Hour Gaps (from 12 to hour hand)
Angle
Type
1:00
1 gap
1 × 30° = 30°
Acute
2:00
2 gaps
2 × 30° = 60°
Acute
3:00
3 gaps
3 × 30° = 90°
Right angle
4:00
4 gaps
4 × 30° = 120°
Obtuse
5:00
5 gaps
5 × 30° = 150°
Obtuse
6:00
6 gaps
6 × 30° = 180°
Straight
7:00
5 gaps (shorter side)
5 × 30° = 150°
Obtuse
8:00
4 gaps (shorter side)
4 × 30° = 120°
Obtuse
9:00
3 gaps (shorter side)
3 × 30° = 90°
Right angle
10:00
2 gaps (shorter side)
2 × 30° = 60°
Acute
11:00
1 gap (shorter side)
1 × 30° = 30°
Acute
12:00
0 gaps
0°
Zero angle
Image needed: A set of 4 clock faces showing different times with the angle between the hands marked: (1) 3:00 = 90° (right angle), (2) 6:00 = 180° (straight angle), (3) 2:00 = 60° (acute), (4) 4:00 = 120° (obtuse). Each clock has the angle arc drawn and labelled with the degree measure and angle type. Style: Clean, colourful clock illustrations, child-friendly, clearly labelled arcs showing the angle Size: 800×400px
Think About It: At 7:00, the hands are 5 hour-gaps apart from the short side (going from 12 clockwise to 7). But wait — shouldn't it be 7 gaps? We always measure the smaller angle (unless the question asks for the reflex angle). Since 7 gaps = 210° (reflex), we take the other side: 360° − 210° = 150° or simply 5 gaps × 30° = 150°.
Key Words
Term
Meaning
Point
An exact location in space, represented by a dot
Line
A straight path extending endlessly in both directions
Ray
A straight path starting at one point and going on forever in one direction
Line Segment
A part of a line with two endpoints and a fixed length
Parallel Lines
Lines that are always the same distance apart and never meet (symbol: ∥)
Intersecting Lines
Lines that cross each other at exactly one point
Perpendicular Lines
Lines that intersect at a right angle — 90° (symbol: ⊥)
Angle
The figure formed when two rays share a common endpoint
Vertex
The common endpoint of the two rays forming an angle
Arms
The two rays that form the sides of an angle
Degree (°)
The unit used to measure angles; a full rotation = 360°
Protractor
A semi-circular instrument used to measure and draw angles
Acute Angle
An angle measuring more than 0° and less than 90°
Right Angle
An angle measuring exactly 90°
Obtuse Angle
An angle measuring more than 90° and less than 180°
Straight Angle
An angle measuring exactly 180° (forms a line)
Reflex Angle
An angle measuring more than 180° and less than 360°
Complete Angle
An angle measuring exactly 360° (full rotation)
Key Points to Remember
A point has no size. A line has no endpoints. A ray has one endpoint. A line segment has two endpoints.
Parallel lines never meet. Perpendicular lines meet at 90°.
An angle is formed by two rays sharing a common vertex.
Angles are measured in degrees (°). A full circle = 360°.
A right angle is marked with a small square (□) at the vertex.
Use a protractor to measure and draw angles. Always check which scale to read!
On a clock, each hour number = 30° apart (since 360° ÷ 12 = 30°).
At 3:00 and 9:00, the hands form a right angle (90°).
At 6:00, the hands form a straight angle (180°).
At 12:00, the hands overlap — angle is 0°.
Finished learning? Now test what you know!
🎯 Quick Quiz — Test Yourself!
Answer these questions right here. You get instant feedback — no paper needed!
Score: 0 / 8
1. An angle exactly equal to 90° is called:
A 90° angle is a right angle.
2. An angle less than 90° is:
An acute angle is greater than 0° but less than 90°.
3. An angle of 145° is:
Between 90° and 180° is obtuse.
4. A straight angle measures:
A straight angle is exactly 180°.
5. A complete angle (full turn) measures how many degrees?
A full turn = 360°.
6. Which instrument is used to measure angles?
A protractor measures angles in degrees.
7. At 3 o'clock, the angle between the two clock hands is how many degrees?
At 3:00 the hands form a right angle = 90°.
8. Two lines that always stay the same distance apart and never meet are called ______ lines.
Parallel lines never meet (like railway tracks).
Practice Questions
A. Identify the type of angle:
1. 45° =
2. 90° =
3. 135° =
4. 180° =
5. 270° =
6. 360° =
B. Estimate the angle and classify:
1. The angle formed by the hands of a clock at 2:00 = (measure) → (type)
2. The angle formed by a fully open pair of scissors = approximately → (type)
3. The angle at the corner of a square = → (type)
4. The angle formed by hands of a clock at 5:00 = → (type)
5. The angle formed by a straight road (no turn) = → (type)
C. Classify as parallel, intersecting, or perpendicular:
1. Two opposite edges of a ruler →
2. The two arms of the letter V →
3. The horizontal and vertical lines in the letter T →
4. Two lanes of a straight highway →
5. The two diagonals of a square →
D. Measure and draw angles:
1. Draw an angle of 60° and label it ∠PQR.
2. Draw an angle of 90° and mark it with the right angle symbol.
3. Draw an angle of 120° and name its type.
4. Draw an angle of 45° and label its vertex and arms.
5. Draw a straight angle (180°) and explain why it looks like a line.
6. Draw an angle of 150° and classify it.
E. Find the angle between the clock hands at these times:
1. 3:00 =
2. 6:00 =
3. 9:00 =
4. 12:00 =
5. 4:00 =
F. Fill in the blanks:
1. An angle less than 90° is called a/an angle.
2. Two lines that never meet are called lines.
3. A has one endpoint and extends endlessly in one direction.
4. Angles are measured in using a protractor.
5. A complete angle measures degrees.
G. True or False:
1. A right angle is exactly 90°.
2. Two parallel lines can sometimes meet if extended far enough.
3. A straight angle looks like a straight line.
4. A reflex angle is smaller than a right angle.
5. All perpendicular lines are intersecting lines.
H. Choose the correct answer (MCQ):
1. An angle of 95° is:
a) Acuteb) Rightc) Obtused) Straight
2. The angle between clock hands at 6:00 is:
a) 90°b) 120°c) 180°d) 360°
3. Which of the following is NOT a type of angle?
a) Acuteb) Parallelc) Obtused) Reflex
4. A protractor can measure angles up to:
a) 90°b) 180°c) 270°d) 360°
I. Word Problems:
1. Arjun wants to cut a pizza into 8 equal slices. What angle will each slice have at the centre? What type of angle is this?
2. A ladder leans against a wall making a 65° angle with the ground. Is this angle acute, right, or obtuse? If the ladder slips and the angle becomes 40°, what type is it now?
3. Priya is making a Rangoli pattern. She needs to draw lines from the centre at equal angles to make 6 equal sections. What angle should each section be?
4. At what time does a clock show a right angle between the hour and minute hands? Name two times when this happens.
Activity — Angle Hunt!
Go on an angle hunt around your house and school! Find at least 8 angles and record them in the table below. Use a protractor to measure as many as you can.
Object / Place
Where the Angle Is
Estimated Angle
Type of Angle
Example: Open book
Between the two covers
About 45°
Acute
Bonus Challenge: Can you find all six types of angles in your house? Write where you found each type:
Acute angle:
Right angle:
Obtuse angle:
Straight angle:
Reflex angle:
Complete angle:
Want to review the lesson again?
Mathematics
Geometry — Lines and Angles
Class 5 | CBSE / NCERT / ICSE
Name: Class: Date:
Learning Objectives
Understand point, line, ray, and line segment
Identify parallel, intersecting, and perpendicular lines
Angles are everywhere — when you open a book, when clock hands move, when a cricket bat swings, and in Indian architecture (Taj Mahal arches, Rangoli patterns, temple gopurams). In this chapter, we learn about points, lines, rays, line segments, types of lines, and dive deep into angles — what they are, how to measure them, and how to find them around us.
Basic Geometric Terms
Term
Endpoints
Length
Symbol
Example
Point
It IS a point
No length
• A
Tip of needle
Line
No endpoints (arrows both sides)
Infinite
↔AB
Horizon
Ray
One endpoint (one arrow)
Infinite in one direction
→AB
Torch beam
Line Segment
Two endpoints
Fixed, measurable
AB (bar)
Edge of ruler
[Image: Comparison diagram — Point, Line, Ray, Line Segment side by side with labels and properties]
Types of Lines
Type
Definition
Symbol
Key Feature
Example
Parallel
Lines that never meet
∥
Always same distance apart
Railway tracks
Intersecting
Lines that cross at one point
—
Form angles
Scissors blades
Perpendicular
Lines meeting at 90°
⊥
Form right angles
Corner of room
[Image: Three diagrams — Parallel lines (railway tracks), Intersecting lines (crossing roads), Perpendicular lines (with square symbol at corner)]
Remember: All perpendicular lines are intersecting lines (they meet at 90°). But not all intersecting lines are perpendicular!
What is an Angle?
An angle is formed when two rays share a common endpoint. The shared endpoint is the vertex. The two rays are the arms. Symbol: ∠
Angles are measured in degrees (°). Full rotation = 360°. Half = 180°. Quarter = 90°.
Types of Angles
Type
Measure
Real-Life Example
Acute
> 0° and < 90°
Clock at 1:00 (30°), pizza slice
Right
Exactly 90°
Corner of book, clock at 3:00
Obtuse
> 90° and < 180°
Clock at 4:00 (120°), reclining chair
Straight
Exactly 180°
Clock at 6:00, ruler lying flat
Reflex
> 180° and < 360°
Larger angle at 10:00 on clock
Complete
Exactly 360°
Full rotation of minute hand
[Image: Six angle diagrams — Acute (<90°), Right (=90° with square), Obtuse (90°–180°), Straight (=180°), Reflex (180°–360°), Complete (=360°)]
Quick Memory Aid: Acute = "cute" small angle | Right = 90° L-shape | Obtuse = "fat" wide angle | Straight = line (180°) | Reflex = past straight | Complete = full circle (360°)
Measuring Angles with a Protractor
A protractor is a semi-circular tool with markings from 0° to 180°. It has an inner scale and an outer scale reading in opposite directions.
Steps to Measure an Angle:
1. Place the centre point of the protractor on the vertex.
2. Align the baseline along one arm of the angle (0° mark).
3. Read where the other arm crosses the scale.
4. Use the scale that starts at 0° from the arm you aligned!
Tip: If the angle looks acute (narrow), the reading must be < 90°. If it looks obtuse (wide), it must be > 90°.
[Image: Step-by-step protractor usage — centre on vertex, baseline on arm, reading at ~60° with labels for inner/outer scale]
Drawing Angles with a Protractor
Steps to Draw an Angle (e.g., 75°):
1. Draw a ray BC (one arm). Mark vertex B.
2. Place protractor — centre on B, baseline along BC.
3. From 0°, count to 75°. Mark point A.
4. Remove protractor. Draw ray BA.
5. Label ∠ABC = 75°. Draw an arc between the arms.
Note: A protractor only goes to 180°. To draw a reflex angle (e.g., 270°), draw 360° − 270° = 90° and mark the reflex (larger) side.
Angles in Real Life
Object / Situation
Approx. Angle
Type
Corner of notebook
90°
Right
Scissors slightly open
20°–30°
Acute
Door open halfway
90°
Right
Door flat against wall
180°
Straight
Pizza slice (8 slices)
45°
Acute
Reclining chair
120°–150°
Obtuse
Clock at 3:00
90°
Right
Clock at 6:00
180°
Straight
Angles on a Clock Face
Clock Rule: 360° ÷ 12 hours = 30° per hour gap. At exact hours, angle = number of gaps × 30° (use shorter side).
Time
Gaps
Angle
Type
1:00
1
30°
Acute
2:00
2
60°
Acute
3:00
3
90°
Right
4:00
4
120°
Obtuse
5:00
5
150°
Obtuse
6:00
6
180°
Straight
9:00
3 (short side)
90°
Right
12:00
0
0°
Zero
[Image: Four clock faces showing 3:00 (90°), 6:00 (180°), 2:00 (60°), 4:00 (120°) with angle arcs labelled]
Key Words
Term
Meaning
Point
Exact location, no size
Line
Extends endlessly in both directions
Ray
One endpoint, extends in one direction
Line Segment
Two endpoints, fixed length
Parallel (∥)
Lines that never meet
Perpendicular (⊥)
Lines meeting at 90°
Vertex
Common endpoint of angle arms
Protractor
Tool to measure/draw angles
Degree (°)
Unit of angle measurement
Key Points:
• Point = no size. Line = infinite. Ray = one end. Segment = two ends.
• Parallel (∥) never meet. Perpendicular (⊥) meet at 90°.
• Angle = two rays sharing a vertex. Measured in degrees.
• Acute < 90° < Right = 90° < Obtuse < 180° = Straight < Reflex < 360° = Complete
• Protractor: centre on vertex, baseline on arm, read correct scale.
• Clock: each hour = 30°. At 3:00 & 9:00 → 90°. At 6:00 → 180°.
Practice Questions
A. Identify the type of angle:
1. 45° =
2. 90° =
3. 135° =
4. 180° =
5. 270° =
6. 360° =
B. Estimate the angle and classify:
1. Clock hands at 2:00 = → Type:
2. Fully open scissors ≈ → Type:
3. Corner of a square = → Type:
4. Clock hands at 5:00 = → Type:
5. Straight road (no turn) = → Type:
C. Classify as parallel, intersecting, or perpendicular:
1. Two opposite edges of a ruler →
2. Two arms of the letter V →
3. Horizontal and vertical lines in letter T →
4. Two lanes of a straight highway →
5. Two diagonals of a square →
D. Measure and draw angles (use a protractor):
1. Draw ∠PQR = 60°
2. Draw a right angle (90°) and mark with □ symbol.
3. Draw an angle of 120° and name its type.
4. Draw ∠XYZ = 45° and label vertex and arms.
5. Draw a straight angle (180°).
6. Draw an angle of 150° and classify it.
E. Find the angle between clock hands:
1. 3:00 =
2. 6:00 =
3. 9:00 =
4. 12:00 =
5. 4:00 =
F. Fill in the blanks:
1. An angle less than 90° is called a/an angle.
2. Two lines that never meet are called lines.
3. A has one endpoint and extends endlessly in one direction.
4. Angles are measured in using a protractor.
5. A complete angle measures degrees.
G. True or False:
1. A right angle is exactly 90°.
2. Parallel lines can meet if extended far enough.
3. A straight angle looks like a straight line.
4. A reflex angle is smaller than a right angle.
5. All perpendicular lines are intersecting lines.
H. Choose the correct answer (MCQ):
1. An angle of 95° is:
a) Acuteb) Rightc) Obtused) Straight
2. The angle between clock hands at 6:00 is:
a) 90°b) 120°c) 180°d) 360°
3. Which is NOT a type of angle?
a) Acuteb) Parallelc) Obtused) Reflex
4. A protractor can measure angles up to:
a) 90°b) 180°c) 270°d) 360°
I. Word Problems:
1. Arjun cuts a pizza into 8 equal slices. What angle does each slice have at the centre? What type of angle is this?
2. A ladder leans against a wall at 65° with the ground. Is this acute, right, or obtuse? If it slips to 40°, what type is it now?
3. Priya makes a Rangoli with 6 equal sections from the centre. What angle is each section?
4. At what two times does a clock show a right angle (90°)?
Activity — Angle Hunt!
Find 8 angles around your house. Estimate the angle and classify each one.
Object
Where the Angle Is
Estimated Angle
Type
Example: Open book
Between covers
~45°
Acute
Bonus: Find all 6 types of angles in your house!
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