Page 167 - ICSE Math 7

In the given figure, ∠1 and ∠2 are adjacent angles
Try This
with Q as the common vertex and ray QR as the x – 2°
If l ⊥ m, find the value of x for the x + 18°
common arm. adjoining figure. Also, find the x + 8° l
supplement of angle x. m
Linear pair

If the sum of the magnitudes of two adjacent angles is 180°, then they are R
known as a linear pair. In the adjoining figure, ∠1 and ∠2 are adjacent
angles forming a linear pair as ∠1 + ∠2 = 180°. 2 1
P Q S
Vertically opposite angles
When two lines intersect at a point, then the angles on the opposite sides of the point P S
of intersection are known as vertically opposite angles. In the adjoining figure, O
lines PQ and RS intersect at O. So, ∠POS and ∠ROQ are vertically opposite
angles. Similarly, ∠POR and ∠SOQ are vertically opposite angles. R Q
Also, ∠POS = ∠ROQ and ∠POR = ∠SOQ
Maths Info
Example 1: One-fourth of the supplement of an angle is 15° less
than its complement. Find the angle. Vertically opposite angles are
Solution: Let the angle be x. always equal.
Supplement of x = 180° – x
Complement of x = 90° – x
According to the question,

1 (180° – x) + 15° = 90° – x
4
(180° – x) + 60° = 90° – x
4
⇒ 180° – x + 60° = 4(90° – x) ⇒ 240° – x = 360° – 4x
⇒ 4x – x = 360° – 240° ⇒ 3x = 120°
120°
⇒ x = = 40°
3
A
Example 2: Find ∠AOB in the adjoining figure. E
Solution: ∠AOB + ∠BOC + ∠COD + ∠DOE + ∠EOA = 360° 15° 85°
(Sum of angles around a point is 360°.) D 80° O
⇒ ∠AOB + 115° + 80° + 15° + 85° = 360° 115° B
⇒ ∠AOB + 295° = 360° C
⇒ ∠AOB = 360° – 295° = 65°

EXERCISE 15.1

1. Write the complement of the following angles.

(a) 65° (b) 20° – x (c) 41°20′45″ (d) 1 of a right angle
2
2. Write the supplement of the following angles.
(a) 85° (b) 45° – x (c) 35°20′ (d) 1 of a complete angle
3

153