Page 166 - ICSE Math 6

Some special angles

Zero angle
If the initial and final position of a ray coincides without making O A(B)
any rotation, then the angle formed is 0°.

Complete angle

If a ray, say OA, makes one complete rotation and then coincides
with its initial position, then the angle formed is known as complete O A(B)
angle and its magnitude is 360°.

Example 1: Find the number of right angles turned through by the hour hand of a clock when it
goes from:
(a) 6 to 12 (b) 4 to 7 (c) 3 to 12
Solution: Looking at the various positions of an hour hand in the reference 11 12 1
clock, we observe: 10 2
(a) rotation from 6 to 12 makes 2 right angles 9 3

(b) rotation from 4 to 7 makes 1 right angle 8 4
7 5
(c) rotation from 3 to 12 makes 3 right angles 6
Example 2: How many right angles do you make if you start facing:

(a) south and turn clockwise to east?
(b) north and turn anti-clockwise to west?
(c) east and turn to east?

Solution: (a) 3 right angles
(b) 1 right angle
(c) 4 right angles (clockwise as well as anti-clockwise)

Example 3: Where will the hour hand of a clock stop if it starts:
(a) from 5 and turns through 1 right angle?
(b) from 7 and turns through 3 right angles?

(c) from 2 and turns through 2 straight angles?
Solution: (a) 8 (b) 4 (c) 2

Example 4: Classify each of the following angles as acute, right, obtuse, straight or reflex.

(a) (b) (c) (d) (e)

Solution: (a) right (b) obtuse (c) reflex (d) straight (e) acute

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