Page 167 - ICSE Math 6

Special pairs of angles

The following are the special pairs of angles.

Congruent angles
A M
Two angles of the same magnitude are called
congruent angles. Here, ∠ABC and ∠MNO are
congruent angles, as ∠ABC = ∠MNO = 30° B 30° C N 30° O

Vertically opposite angles
A
The angles formed by two intersecting lines (or line segments) without
any common arm are called vertically opposite angles. Vertically C m y B
opposite angles are always equal. Here, ∠m and ∠n and ∠x and ∠y x n
are the two pairs of vertically opposite angles. Also, ∠m = ∠n and
∠x = ∠y. B

Complementary angles A
Two angles are called complementary angles if the P
sum of their measures is 90°. Here, ∠ABC + ∠PQR
= 60° + 30° = 90°, so they are complementary angles. B 60° 30°
C Q R
Supplementary angles
Two angles are called supplementary angles if the sum A P
of their measures is 180°. Here, ∠ABC + ∠PQR =
120° + 60° = 180°, so they are supplementary angles. 120°
B C Q 60° R
Adjacent angles
A B
Two angles lying on the opposite sides of a common arm and having the
same vertex are called adjacent angles. Here, ∠AOB and ∠BOC are adjacent
angles.
D C
Linear pair
C
Two adjacent supplementary angles form a linear pair. Here, ∠AOC and
∠BOC form a linear pair.
B O A

EXERCISE 15.1

1. In the adjoining figure, name the points which are:
(a) in the interior of ∠ABC A P S C
(b) in the exterior of ∠ABC T

(c) on the boundary of ∠ABC R B Q C
2. Sort out the angles 5°, 65°, 96°, 190°, 170° and 320° as acute, obtuse or reflex.
3. Name the acute angles made on line segment AB in the adjoining D
figure.
A B

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