Page 154 - Maths Skills - 7

152 Maths

Zero angle
An angle whose arms coincide with each other without taking any
rotation is called zero angle.
Complete angle

An angle whose arms coincide with each other after taking
a complete rotation is a complete angle. ∠AOB is a complete 360º
angle. Its measure is 360°.

Reflex angle
An angle whose measure is more than 180° but less than 360° is called a reflex angle.
Shaded region ∠AOB is a reflex angle.

PAIR OF ANGLES

Complementary Angles C
If the sum of the measures of two angles is 90°, then the angles are said to be complementary
angles. Each angle is said to be the complement to the other. B
In Fig., ∠AOB + ∠BOC = 90°.
\ ∠AOB and ∠BOC are complementary angles. O A

Supplementary Angles
If the sum of the measures of two angles is 180°, then the angles are said to B
be supplementary angles. Each angle is said to be the supplement of the other.
In Fig, ∠AOB + ∠BOC = 180°.

\ ∠AOB and ∠BOC are supplementary angles. C O A

Adjacent Angles
Two angles in a plane are said to be adjacent angles if they have
(i) a common vertex; (ii) a common arm; and C

(iii) their other two arms lie on the opposite sides of the common arm. B
In Fig., ∠AOB and ∠BOC are adjacent. They have a common vertex ‘O’ and a common arm

OB . The other two arms OA andOC lie on the opposite sides of the common arm OB . O A

Linear Pair Angles
A pair of adjacent angles is said to form a linear pair of angles, if their two non-common arms form a straight line
(or are opposite rays).
In Fig., ∠AOB and ∠BOC form a linear pair since the non-common arms B

OA andOC lie on the same line.
Thus, the sum of the measures of a linear pair is always 180°.
C O A
A
D Vertically Opposite Angles
2 Two angles formed by two intersecting lines which have no common arm, are called vertically
3 1 opposite angles.
4
O Intersection of two lines means two straight lines crossing each other at some angle as shown
C B in Fig.