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Quick Check
1. Identify the following type of angles.

(a) (b) (c) (d)
2. In the given diagram, name the acute angle, right angle and obtuse angles.

A E
D
B C

Example 11: How many degrees are there in

(a) 1 of a straight angle (b) 4 of a right angle
4 5
1 1
Solution: (a) of a straight angle = × 180° = 45°
4 4

4 4
(b) of a right angle = × 90° = 72°
5 5
Example 12: Find the number of right angles turned through by the hour hand of a clock when
it goes from:

(a) 1 to 7 (b) 12 to 9

Solution: The hour hand completes 1 revolution (12 hours) and makes one complete angle.

(a) From 1 to 7 11 12 1
10 2
= 6 hours 9 3
8 4
6 7 6 5
In 6 hours, it will turn through = × 360° = 180° = 2 right angles.
12

(b) From 12 to 9
= 9 hours 11 12 1
10 2
9 9 3
In 9 hours, it will turn through = × 360° = 270° = 3 right angles. 8 4
12 7 6 5

Example 13: What fraction of a revolution clockwise does the hour hand of a clock turn through,
when it goes from:

(a) 4 to 10? (b) 5 to 8?
Solution: 1 revolution = 360°

180° 1
(a) From 4 to 10, it will turn through 180° = = of a revolution
360° 2

90° 1
(b) From 5 to 8, it will turn through 90° = = of a revolution.
360° 4

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