Adjacent Angles & Linear Pair (āĻ¸āĻ¨ā§āĻ¨āĻŋāĻšāĻŋāĻ¤ āĻā§āĻŖ āĻā§°ā§ ā§°ā§āĻāĻŋāĻ āĻā§āĻŖāĻ¯ā§ā§°)
Adjacent Angles (āĻ¸āĻ¨ā§āĻ¨āĻŋāĻšāĻŋāĻ¤ āĻā§āĻŖ)
Two angles are adjacent if they have a common vertex, a common arm, and their non-common arms lie on either side of the common arm.
āĻ¯āĻŋ āĻĻā§āĻāĻž āĻā§āĻŖā§° āĻāĻāĻž āĻ¸āĻžāĻ§āĻžā§°āĻŖ āĻļā§ā§°ā§āĻˇāĻŦāĻŋāĻ¨ā§āĻĻā§ (Vertex), āĻāĻāĻž āĻ¸āĻžāĻ§āĻžā§°āĻŖ āĻŦāĻžāĻšā§ (Arm) āĻĨāĻžāĻā§ āĻā§°ā§ āĻŦāĻžāĻā§ āĻŦāĻžāĻšā§āĻĻā§āĻāĻž āĻ¸āĻžāĻ§āĻžā§°āĻŖ āĻŦāĻžāĻšā§ā§° āĻĻā§āĻ¯āĻŧā§āĻĢāĻžāĻ˛ā§ āĻĨāĻžāĻā§, āĻ¸ā§āĻ āĻā§āĻŖāĻ¯ā§ā§°āĻ āĻ¸āĻ¨ā§āĻ¨āĻŋāĻšāĻŋāĻ¤ āĻā§āĻŖ (Adjacent Angles) āĻŦā§āĻ˛āĻž āĻšāĻ¯āĻŧāĨ¤
Example | āĻāĻĻāĻžāĻšā§°āĻŖ: ∠AOB and ∠BOC are adjacent angles.
∠AOB āĻā§°ā§ ∠BOC āĻ¸āĻ¨ā§āĻ¨āĻŋāĻšāĻŋāĻ¤ āĻā§āĻŖāĨ¤
Linear Pair (ā§°ā§āĻāĻŋāĻ āĻā§āĻŖāĻ¯ā§ā§°)
A linear pair is a pair of adjacent angles whose non-common arms are opposite rays.
āĻ¯āĻŋ āĻ¸āĻ¨ā§āĻ¨āĻŋāĻšāĻŋāĻ¤ āĻā§āĻŖāĻ¯ā§ā§°ā§° āĻ
āĻ¸āĻžāĻ§āĻžā§°āĻŖ āĻŦāĻžāĻšā§āĻĻā§āĻāĻž āĻŦāĻŋāĻĒā§°ā§āĻ¤ ā§°āĻļā§āĻŽāĻŋ āĻšāĻ¯āĻŧ, āĻ¤āĻžāĻ ā§°ā§āĻāĻŋāĻ āĻā§āĻŖāĻ¯ā§ā§° (Linear Pair) āĻŦā§āĻ˛āĻž āĻšāĻ¯āĻŧāĨ¤
Property | āĻŦā§āĻļāĻŋāĻˇā§āĻā§āĻ¯
The sum of the angles in a linear pair is 180°. (ā§°ā§āĻāĻŋāĻ āĻā§āĻŖāĻ¯ā§ā§°ā§° āĻā§āĻŖ āĻĻā§āĻāĻžā§° āĻ¯ā§āĻāĻĢāĻ˛ āĻ¸āĻĻāĻžāĻ¯āĻŧ 180°āĨ¤)
In the figure, ∠AOB + ∠BOC = 180°. (āĻāĻŋāĻ¤ā§ā§°āĻ¤, ∠AOB + ∠BOC = 180°āĨ¤)
MCQs
1. Two angles having a common vertex and a common arm are called ______. / āĻāĻāĻž āĻ¸āĻžāĻ§āĻžā§°āĻŖ āĻļā§ā§°ā§āĻˇāĻŦāĻŋāĻ¨ā§āĻĻā§ āĻā§°ā§ āĻāĻāĻž āĻ¸āĻžāĻ§āĻžā§°āĻŖ āĻŦāĻžāĻšā§ āĻĨāĻāĻž āĻĻā§āĻāĻž āĻā§āĻŖāĻ āĻāĻŋ āĻŦā§āĻ˛āĻž āĻšāĻ¯āĻŧ ?
(a) Complementary angles (b) Adjacent angles (c) Vertically opposite angles (d) Alternate angles
Ans: (b) Adjacent angles
2. A linear pair consists of ______. / ā§°ā§āĻāĻŋāĻ āĻā§āĻŖāĻ¯ā§ā§° āĻāĻŋāĻšā§ āĻāĻ āĻŋāĻ¤?
(a) Two adjacent angles (b) Two equal angles (c) Two right angles (d) Two acute angles
Ans: (a) Two adjacent angles
3. The sum of the angles in a linear pair is ______. / ā§°ā§āĻāĻŋāĻ āĻā§āĻŖāĻ¯ā§ā§°ā§° āĻā§āĻŖ āĻĻā§āĻāĻžā§° āĻ¯ā§āĻāĻĢāĻ˛ āĻāĻŋāĻŽāĻžāĻ¨ ?
(a) 90° (b) 180° (c) 270° (d) 360°
Ans: (b) 180°
4. If one angle of a linear pair is 70°, the other angle is ______. / āĻ¯āĻĻāĻŋ ā§°ā§āĻāĻŋāĻ āĻā§āĻŖāĻ¯ā§ā§°ā§° āĻāĻāĻž āĻā§āĻŖ 70° āĻšāĻ¯āĻŧ, āĻāĻ¨āĻā§ āĻā§āĻŖ āĻāĻŋāĻŽāĻžāĻ¨ ?
(a) 70° (b) 90° (c) 110° (d) 120°
Ans: (c) 110°
5. Adjacent angles have a common ______. / āĻ¸āĻ¨ā§āĻ¨āĻŋāĻšāĻŋāĻ¤ āĻā§āĻŖā§° āĻāĻāĻž āĻ¸āĻžāĻ§āĻžā§°āĻŖ ______ āĻĨāĻžāĻā§āĨ¤
(a) Vertex and arm (b) Side only (c) Angle only (d) Ray only
Ans: ((a) Vertex and arm