Measuring Angles with Protractor
An angle is formed when two rays meet at a common point. The amount of turn between the two rays is measured in degrees (°).
A protractor is the tool used to measure and draw angles. It is a D-shaped (semicircular) instrument with markings from 0° to 180°.
In Class 6, you will learn how to read a protractor correctly and use it to measure or draw angles of any size.
What is Measuring Angles with Protractor - Grade 6 Maths (Understanding Elementary Shapes)?
Definition: A protractor is a semicircular instrument used to measure angles in degrees.
Parts of a protractor:
- Baseline (straight edge): The flat bottom edge of the protractor.
- Centre point: The small mark or hole at the middle of the baseline.
- Inner scale: Numbers from 0° to 180° going left to right.
- Outer scale: Numbers from 0° to 180° going right to left.
Important: The protractor has two scales (inner and outer). You must choose the correct one based on where your angle's ray starts from 0°.
Measuring Angles with Protractor Formula
Steps to measure an angle using a protractor:
- Place the centre point of the protractor on the vertex of the angle.
- Align the baseline along one ray of the angle.
- That ray should pass through the 0° mark on one of the scales.
- Read the number where the other ray crosses the scale.
- Use the scale that starts from 0° on the first ray.
Steps to draw an angle of a given measure:
- Draw a ray OA using a ruler.
- Place the protractor with centre on O and baseline along OA.
- Find the required angle (say 65°) on the correct scale. Mark a point B at that position.
- Remove the protractor. Join O to B.
- ∠AOB = 65°.
How to pick the right scale:
- If the ray passes through 0° on the inner scale, read the angle on the inner scale.
- If the ray passes through 0° on the outer scale, read the angle on the outer scale.
- Quick check: If the angle looks like it is less than 90° (acute), the reading should be less than 90°. If it looks greater than 90° (obtuse), the reading should be more than 90°.
Types and Properties
Types of angles (based on measurement):
- Acute angle: Greater than 0° but less than 90°.
- Right angle: Exactly 90°.
- Obtuse angle: Greater than 90° but less than 180°.
- Straight angle: Exactly 180° (a straight line).
- Reflex angle: Greater than 180° but less than 360°.
- Complete angle: Exactly 360° (full rotation).
Measuring reflex angles:
- A protractor only goes up to 180°. So you cannot directly measure a reflex angle.
- Measure the non-reflex part (the smaller angle). Call it x°.
- Reflex angle = 360° − x°.
Solved Examples
Example 1: Measuring an Acute Angle
Problem: Measure ∠PQR where one ray QP is along the baseline and the other ray QR crosses the protractor at 55° on the inner scale.
Solution:
The baseline ray passes through 0° on the inner scale. So we read the inner scale.
The other ray crosses at 55°.
Answer: ∠PQR = 55° (acute angle).
Example 2: Measuring an Obtuse Angle
Problem: One ray is along the baseline at 0° (outer scale). The other ray crosses at 130° on the outer scale. What is the angle?
Solution:
Since we start from 0° on the outer scale, read the outer scale.
Answer: The angle is 130° (obtuse angle).
Example 3: Choosing the Correct Scale
Problem: A student reads an angle as both 60° and 120° from the two scales. The angle looks like it is less than a right angle. Which reading is correct?
Solution:
The angle looks less than 90° (acute). So 120° cannot be correct.
Answer: The correct measurement is 60°.
Example 4: Drawing a 75° Angle
Problem: Draw an angle of 75°.
Solution:
- Draw a ray OA.
- Place the protractor with centre at O and baseline along OA.
- Starting from 0° on the scale, find 75°. Mark the point as B.
- Remove the protractor. Join OB.
Answer: ∠AOB = 75°.
Example 5: Finding a Reflex Angle
Problem: The smaller angle between two rays is 110°. Find the reflex angle.
Solution:
Reflex angle = 360° − 110° = 250°
Answer: The reflex angle is 250°.
Example 6: Measuring a Right Angle
Problem: The corner of a book forms an angle. Measure it with a protractor.
Solution:
When you place the protractor, the ray crosses exactly at 90°.
Answer: The angle is 90° (a right angle).
Example 7: Drawing a Straight Angle
Problem: Draw a straight angle.
Solution:
- Draw a ray OA.
- Place protractor at O along OA. Mark the point at 180°. Call it B.
- Join OB. Points B, O, A are in a straight line.
Answer: ∠AOB = 180°.
Example 8: Finding Missing Angle on a Straight Line
Problem: Two angles on a straight line are x° and 125°. Find x.
Solution:
Angles on a straight line add up to 180°.
x + 125 = 180
x = 180 − 125 = 55°
Answer: x = 55°.
Real-World Applications
Where angle measurement is used:
- Construction: Builders measure angles for roofs, staircases, and pillars.
- Clocks: The hands of a clock form different angles at different times.
- Maps and navigation: Pilots and sailors use angles to find direction.
- Sports: The angle of a cricket bat, a ramp, or a goalpost matters in games.
- Art: Designers use angles to create patterns and shapes.
Key Points to Remember
- A protractor measures angles from 0° to 180°.
- Always place the centre point on the vertex and the baseline along one ray.
- A protractor has two scales — inner and outer. Use the one that starts at 0° on your ray.
- Quick check: If the angle looks acute, the reading must be less than 90°.
- To draw an angle, use a ray, protractor, and mark the degree point.
- For a reflex angle, measure the smaller angle and subtract from 360°.
- A straight angle = 180°, a right angle = 90°, a complete angle = 360°.
- Angles on a straight line add up to 180°.
Practice Problems
- Measure the angle at the corner of your notebook. What type of angle is it?
- Draw angles of 45°, 90°, 120°, and 160° using a protractor.
- The non-reflex angle between two rays is 85°. What is the reflex angle?
- Two angles on a straight line are 72° and x°. Find x.
- A protractor shows readings of 40° (inner) and 140° (outer). The angle looks acute. Which reading is correct?
- Draw a straight angle (180°) and mark a ray in the middle to create two angles. Measure both.
Frequently Asked Questions
Q1. What is a protractor?
A protractor is a D-shaped (semicircular) tool used to measure and draw angles. It has markings from 0° to 180° in two scales — inner and outer.
Q2. Why does a protractor have two scales?
The two scales let you measure angles from either direction. If the ray is on the left, you use one scale. If the ray is on the right, you use the other. This avoids flipping the protractor.
Q3. How do I know which scale to read?
Check which scale shows 0° where your first ray (baseline ray) is. Read the angle on that same scale. Also check: if the angle looks acute (small), the number should be less than 90°.
Q4. Can I measure a reflex angle with a protractor?
Not directly, because a protractor only goes up to 180°. Measure the smaller angle (non-reflex part) and subtract from 360° to get the reflex angle.
Q5. What is the smallest angle I can measure?
Most school protractors can measure angles as small as 1°. The smallest markings on the protractor represent 1° each.
Q6. What unit is used to measure angles?
Angles are measured in degrees, written with the symbol °. A full rotation is 360°, a half rotation is 180°, and a quarter rotation is 90°.
