Drawing Angles
Drawing angles is an important geometry skill in Class 4. Using a protractor, you can construct angles of any given measure. Accurate angle drawing is needed in geometry constructions, map reading, and design work.
Before drawing angles, you should know how to identify and measure them. An angle is formed when two rays share a common endpoint (called the vertex).
What is Drawing Angles - Class 4 Maths (Geometry)?
An angle is the amount of turn between two rays that share a common endpoint.
Tools needed: Protractor, pencil, ruler.
Steps to Draw an Angle
- Draw a base ray (a straight line with an endpoint).
- Place the centre of the protractor at the endpoint (vertex).
- Align the base line of the protractor with the ray.
- Find the required degree mark on the protractor and place a dot.
- Remove the protractor and draw a ray from the vertex through the dot.
Types and Properties
Types of angles by measure:
| Angle Type | Measure | Example |
|---|---|---|
| Acute angle | Less than 90° | 30°, 45°, 60° |
| Right angle | Exactly 90° | 90° |
| Obtuse angle | Between 90° and 180° | 120°, 135°, 150° |
| Straight angle | Exactly 180° | 180° |
Solved Examples
Example 1: Example 1: Drawing a 60° Angle
Problem: Draw an angle of 60°.
Solution:
Step 1: Draw a base ray AB.
Step 2: Place the protractor centre at A, aligning the base line with ray AB.
Step 3: Find 60° on the inner scale. Mark a point C.
Step 4: Remove the protractor. Draw ray AC.
Answer: Angle BAC = 60° (an acute angle).
Example 2: Example 2: Drawing a 90° Angle (Right Angle)
Problem: Draw a right angle.
Solution:
Step 1: Draw a base ray PQ.
Step 2: Place protractor at P, aligned with PQ.
Step 3: Find 90° on the protractor. Mark point R.
Step 4: Draw ray PR.
Answer: Angle QPR = 90°. Mark the right angle symbol (a small square) at the vertex.
Example 3: Example 3: Drawing a 120° Angle
Problem: Draw an angle of 120°.
Solution:
Step 1: Draw a base ray XY.
Step 2: Place protractor at X. Find 120° on the outer scale (since it is greater than 90°).
Step 3: Mark a dot at 120°. Call it Z.
Step 4: Draw ray XZ.
Answer: Angle YXZ = 120° (an obtuse angle).
Example 4: Example 4: Drawing a 45° Angle
Problem: Draw an angle of 45°.
Solution:
Step 1: Draw a base ray.
Step 2: Using the protractor, mark 45° and draw the second ray.
Answer: A 45° angle is exactly half of a right angle.
Example 5: Example 5: Drawing a 180° Angle (Straight Angle)
Problem: Draw a straight angle.
Solution:
Step 1: Draw a base ray AB.
Step 2: Extend the ray in the opposite direction through A, forming ray AC.
Answer: Angle BAC = 180°. The two rays form a straight line.
Example 6: Example 6: Which Scale to Use?
Problem: You want to draw 135°. Which protractor scale do you read — inner or outer?
Solution:
Step 1: 135° > 90°, so it is an obtuse angle.
Step 2: If your base ray points right and you measure counter-clockwise, use the outer scale. If you measure clockwise from the base, use the inner scale that starts at 0° at your base ray.
Answer: Use the scale that starts at 0° along your base ray, and read up to 135°.
Example 7: Example 7: Drawing a 30° Angle
Problem: Draw an angle of 30°.
Solution:
Step 1: Draw a base ray. Place protractor. Mark 30°.
Step 2: Draw the second ray through the mark.
Answer: A 30° acute angle.
Example 8: Example 8: Drawing a 150° Angle
Problem: Draw an angle of 150°.
Solution:
Step 1: Draw a base ray. Place protractor aligned with the ray.
Step 2: Count from 0° along the correct scale to 150°. Mark a dot.
Step 3: Draw the second ray.
Answer: A 150° obtuse angle.
Example 9: Example 9: Word Problem — Clock Hands
Problem: At 3 o'clock, the minute hand points at 12 and the hour hand at 3. What angle do they form? Draw it.
Solution:
Step 1: From 12 to 3 is a quarter turn = 360° ÷ 4 = 90°.
Step 2: Draw a 90° angle using a protractor.
Answer: The hands form a 90° angle (right angle).
Key Points to Remember
- An angle is measured in degrees (°).
- Use a protractor to draw accurate angles.
- Always align the centre of the protractor with the vertex and the base line with the ray.
- Read the correct scale — the one that starts at 0° along your base ray.
- Acute angles are less than 90°; right angles are 90°; obtuse angles are between 90° and 180°.
- A full turn = 360°, a half turn = 180°, a quarter turn = 90°.
Practice Problems
- Draw an angle of 75° using a protractor.
- Draw a right angle and label it.
- Draw an angle of 110°. Is it acute or obtuse?
- Draw an angle of 40° and another of 140°. What do you notice about their sum?
- What angle do the clock hands make at 6 o'clock? Draw it.
- Draw a straight angle (180°).
- Draw a 55° angle and measure it with a protractor to verify.
Frequently Asked Questions
Q1. What tool is used to draw angles?
A protractor is used to draw angles. It is a semicircular tool marked with degrees from 0° to 180°.
Q2. How do you know which protractor scale to read?
Use the scale that starts at 0° along your base ray. If the 0° mark is on the right and you are measuring counter-clockwise, use the inner scale.
Q3. What is the difference between acute and obtuse angles?
An acute angle measures less than 90°. An obtuse angle measures more than 90° but less than 180°. A 90° angle is called a right angle.
Q4. Can you draw an angle without a protractor?
Some special angles (60°, 90°, 120°) can be drawn using a compass and ruler. But for general angles, a protractor is needed.
Q5. What is a straight angle?
A straight angle measures exactly 180°. The two rays form a straight line.
Q6. What is a full angle?
A full angle (or complete angle) measures 360°. It represents one complete rotation.
Q7. Why is drawing angles important?
Drawing angles accurately is needed in geometry constructions, making maps, designing buildings, and in various engineering and art applications.
Q8. Is drawing angles part of NCERT Class 4?
Yes, drawing and measuring angles using a protractor is part of the CBSE/NCERT Class 4 Maths curriculum under the Geometry chapter.
