Measuring Angles

Class 6 Maths · Chapter 2: Lines and Angles · NCERT Ganita Prakash section 2.9

Learn

To give an angle a number, mathematicians divided the full turn around a point into 360 equal parts. Each part is 1 degree, written 1°. Here each slice is 10°, so three slices make 30°.

3 × 10° = 30°

A full turn is 360°. A straight angle is half a turn: 180°. A right angle is half of a straight angle: 90°.

360° → 180° → 90°

Why 360? People long ago counted about 360 days in a year, and 360 is a friendly number: it can be split equally into 2, 3, 4, 5, 6, 8, 9, 10 or 12 parts.

360 ÷ 12 = 30°

A protractor is a half circle divided into 180 degrees. Put its centre on the vertex, line up one arm with 0, and read where the other arm crosses the scale. Long marks are every 10°, middle marks every 5°.

50°

A protractor has two rows of numbers: one starts at 0 on the right, the other at 0 on the left. Always count from the 0 that your base arm lines up with.

130° (not 50°)

Use the protractor: make an angle of 135°.

Fold a paper circle in half again and again: you get 180°, 90°, 45°, 22.5° … Each fold cuts an angle into two equal halves. This is called bisecting the angle, and the crease is the angle bisector.

90° ÷ 2 = 45°

Remember

• 1 full turn = 360°. Straight angle = 180°. Right angle = 90°.
• Protractor: centre on the vertex, one arm on 0, read on the same row of numbers.
• Bisect means cut into two equal halves; the line that does it is the angle bisector.

Quick check

How many degrees are in a right angle?

1. 45°
2. 90°
3. 180°
4. 360°

Think about it

At 4 o'clock, what is the smaller angle between the two hands of a clock?

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.