Measuring Angles with Protractor
To find the exact size of an angle, we use a tool called a protractor. A protractor is a semi-circular instrument marked from 0° to 180°.
In Class 4, you will learn how to place a protractor correctly, read the scale, and measure angles accurately in degrees.
What is Measuring Angles with Protractor - Class 4 Maths (Geometry)?
A protractor is a D-shaped measuring tool used to measure and draw angles in degrees (°).
It has two scales — an inner scale (reads left to right, 0° to 180°) and an outer scale (reads right to left, 0° to 180°). The small hole or mark at the centre of the straight edge is called the centre point (or baseline mark).
Measuring Angles with Protractor Formula
Steps to Measure an Angle
1. Place the centre point on the vertex.
2. Align the baseline with one arm.
3. Read the degree where the other arm crosses the scale.
Which scale to read? If the angle opens to the right, use the inner scale (starting from 0° on the right). If the angle opens to the left, use the outer scale (starting from 0° on the left). Always start reading from 0°, not from 180°.
Types and Properties
After measuring, verify the angle type:
| Measurement | Type |
|---|---|
| Between 0° and 90° | Acute angle |
| Exactly 90° | Right angle |
| Between 90° and 180° | Obtuse angle |
| Exactly 180° | Straight angle |
After measuring, always check: does the angle look acute or obtuse? If you measured 150° but the angle looks small, you probably read the wrong scale.
Solved Examples
Example 1: Example 1: Measuring an acute angle
Problem: Measure an angle where one ray points right and the other slants upward.
Solution:
Step 1: Place the centre point of the protractor on the vertex.
Step 2: Align the baseline with the horizontal ray.
Step 3: The other ray crosses the inner scale at 55°.
Answer: The angle measures 55° (acute angle).
Example 2: Example 2: Measuring an obtuse angle
Problem: Measure an angle that opens wide between two rays.
Solution:
Step 1: Place the centre of the protractor on the vertex.
Step 2: Align the baseline with one arm.
Step 3: The other arm crosses the scale at 130°.
Step 4: 130° is between 90° and 180°, so it matches the wide opening.
Answer: The angle measures 130° (obtuse angle).
Example 3: Example 3: Right angle check
Problem: Aditi measures the corner of her notebook with a protractor. What should the reading be?
Solution:
Step 1: Place the protractor at the corner.
Step 2: Align the baseline along one edge.
Step 3: The other edge crosses the scale at exactly 90°.
Answer: The corner measures 90° — a right angle.
Example 4: Example 4: Choosing the correct scale
Problem: Kavi measures an angle. The second arm crosses at a marking where the inner scale shows 40° and the outer scale shows 140°. The angle looks small. Which reading is correct?
Solution:
Step 1: The angle looks small, so it should be acute (less than 90°).
Step 2: 40° is acute. 140° is obtuse.
Answer: The correct measurement is 40°. Read the scale that starts from 0° at the baseline arm.
Example 5: Example 5: Drawing an angle of 75°
Problem: Draw an angle of 75° using a protractor.
Solution:
Step 1: Draw a ray (one arm) using a ruler.
Step 2: Place the centre point of the protractor on the endpoint of the ray.
Step 3: Align the baseline with the ray.
Step 4: Starting from 0°, count along the scale to 75°. Mark a dot.
Step 5: Remove the protractor. Join the endpoint to the dot.
Answer: The angle drawn is 75°.
Example 6: Example 6: Finding a missing angle in a triangle
Problem: Ria draws a triangle and measures two angles as 65° and 50°. What is the third angle?
Solution:
Step 1: Sum of angles in a triangle = 180°.
Step 2: Third angle = 180° − 65° − 50° = 65°.
Step 3: Ria can verify by measuring the third angle with a protractor.
Answer: The third angle is 65°.
Example 7: Example 7: Comparing two angles
Problem: Dev measures angle A as 85° and angle B as 95°. Which is larger? Classify each.
Solution:
Step 1: 85° < 90° → angle A is acute.
Step 2: 95° > 90° → angle B is obtuse.
Step 3: 95° > 85°, so angle B is larger.
Answer: Angle B (95°) is larger. A is acute; B is obtuse.
Example 8: Example 8: Drawing a right angle
Problem: Draw an angle of exactly 90° using a protractor.
Solution:
Step 1: Draw a horizontal ray.
Step 2: Place the protractor's centre on the endpoint of the ray.
Step 3: Align the baseline. Mark a dot at 90° on the scale.
Step 4: Join the endpoint to the dot. Draw the small square symbol at the vertex.
Answer: A right angle (90°) is drawn.
Example 9: Example 9: Estimating before measuring
Problem: Before using the protractor, Neha estimates an angle is about 110°. After measuring, she reads 108°. Is her estimate reasonable?
Solution:
Step 1: Estimate = 110°, actual = 108°.
Step 2: Difference = 110° − 108° = 2°.
Answer: Yes, Neha's estimate of 110° is very close to the actual 108°. Her estimation is excellent.
Real-World Applications
Measuring angles is useful in many real-life tasks:
- Drawing geometric shapes — accurate triangles and quadrilaterals need precise angles.
- Map reading — finding direction involves angles from a reference line.
- Construction — builders measure angles to cut materials and fix structures.
- Art and rangoli — patterns with equal angles look symmetrical and beautiful.
Key Points to Remember
- A protractor measures angles in degrees (°).
- Place the centre point on the vertex and the baseline along one arm.
- Read the scale starting from 0° at the baseline arm.
- Use the inner scale for angles opening right, outer scale for angles opening left.
- If the angle looks small, the reading must be less than 90°.
- To draw an angle: draw a ray → place protractor → mark degree → join.
- Always estimate before measuring to catch errors.
- The sum of angles in a triangle is always 180°.
Practice Problems
- Place your protractor on the corner of your desk. What angle do you read?
- Draw an angle of 60° using a protractor and label it as acute or obtuse.
- An angle reads 35° on the inner scale and 145° on the outer scale. The angle looks small. Which reading is correct?
- Draw a triangle and measure all three angles. Check if they add up to 180°.
- Draw an angle of 150°. Classify it.
- Arjun says the angle formed by a fully open book lying flat on a table is 180°. Is he correct? Why?
- Measure the angle between the hour and minute hands on a clock showing 4 o'clock. What type of angle is it?
Frequently Asked Questions
Q1. What is a protractor used for?
A protractor is used to measure and draw angles in degrees. It is a semi-circular tool marked from 0° to 180°.
Q2. Why does a protractor have two scales?
The two scales let you measure angles opening in either direction — left or right. You always read the scale that starts from 0° at the arm on the baseline.
Q3. How do I know which scale to read?
Find the arm on the baseline. Read the scale showing 0° at that arm. If the angle looks acute, the reading must be less than 90°. If it looks obtuse, the reading must be more than 90°.
Q4. Can a protractor measure angles greater than 180°?
A standard protractor measures up to 180°. For reflex angles (greater than 180°), measure the smaller angle and subtract it from 360°.
Q5. What is the smallest angle a protractor can measure?
Most school protractors show markings every 1°, so the smallest readable angle is 1°. Very tiny angles are hard to measure accurately.
Q6. How do you draw an angle without a protractor?
You can fold paper to make 90° (right angle) or 45° angles. For other precise angles, a protractor is necessary.
Q7. Why should I estimate before measuring?
Estimating helps you catch mistakes. If you expect about 60° but read 120°, you likely read the wrong scale.
Q8. What does the degree symbol (°) mean?
The degree symbol is the unit for measuring angles. A full circle has 360°, a straight angle has 180°, and a right angle has 90°.
Q9. Can I check a right angle without a protractor?
Yes. Use the corner of a sheet of paper — it is a right angle (90°). Place it against the angle you want to check. If the edges match perfectly, the angle is 90°.
