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Adjacent Angles

Two angles in a plane are said to be adjacent if they have a common Common
arm
vertex and a common arm in between the other two arms. A
In the adjoining figure, ∠AOB and ∠BOC are two adjacent angles having B
common vertex O, and common arm OB. Other two arms OA and OC are Common
Vertex
on either side of the common arm OB.
O C
\ ∠AOC = ∠AOB + ∠BOC
Linear Pair of Angles

If the sum of two adjacent angles is equal to 180°, then they are called the D
linear pair of angles.
60° 120°
In the adjacent figure, ∠ACD = 120° and ∠BCD = 60°, then,
B C A
∠ACB = ∠ACD + ∠BCD = 120° + 60° = 180°

Since, the sum of ∠ACD and ∠BCD is equal to 180°, so they form a linear pair.
Vertically Opposite Angles

When two lines intersect each other at a point, two sets of opposite angles
are formed and each pair of opposite angles is called vertically opposite A D
angles. When two lines intersect each other, the vertically opposite angles O
so formed are equal. In the adjoining figure, two lines AC and BD intersect
each other at point O. B C
∠AOB and ∠COD form a pair of vertically opposite angles, and Remember
∠AOD and ∠BOC form the other pair of vertically opposite angles. A linear pair is a pair of adjacent

Since, the vertically opposite angles are equal. Therefore, angles whose non-common sides
are opposite rays.
∠AOB = ∠COD and ∠AOD = ∠BOC

Practice Time 7A

1. Identify whether the following pair of angles are complementary or supplementary.

(a) 63°, 117° (b) 59°, 31° (c) 121°, 59° (d) 90°, 90°
(e) 12°, 168° (f) 27°, 63°
2. Find the complementary angle of the given angles.
1
(a) 22° (b) 15 ° (c) 43° (d) 32.5°
2
3. Find the supplementary angle of the following angles.
(a) 83° (b) 109° (c) 37° (d) 144°
4. In the given figures, identify the adjacent angles, linear pair of angles and vertically opposite angles.

(a) (b) 2 (c) 1 (d)
R P A 1 4 3 4 2 z y
5 6 3 x
O 6 5 w
Q S B

153 Lines and Angles