Each figure given below shows a pair of adjacent angles AOB and BOC. F

1.	Each figure given below shows a pair of adjacent angles AOB and BOC. Find whether or not the exterior arms OA and OC are in the same straight line.
Answer» (i) ∠AOB + ∠COB = 180° Since, the sum of adjacent angles AOB and COB = 180° (90° - x) + (90°+ x) = 180° ⇒ 90°-x + 90° + x = 180° ⇒ 180° =180° The exterior arms. OA and OC are in the same straight line. (ii) ∠AOB + ∠BOC = 97° + 83° = 180° ⇒ The sum of adjacent angles AOB and BOC is 180°. ∴ The exterior arms OA and OC are in the same straight line. (iii)∠COB + ∠AOB = 88° + 112° = 200° ; which is not 180°. ⇒ The exterior amis OA and OC are not in the same straight line.

Each figure given below shows a pair of adjacent angles AOB and BOC. Find whether or not the exterior arms OA and OC are in the same straight line.

Answer»

(i) ∠AOB + ∠COB = 180°

Since, the sum of adjacent angles AOB and COB = 180°

(90° - x) + (90°+ x) = 180°

⇒ 90°-x + 90° + x = 180°

⇒ 180° =180°

The exterior arms. OA and OC are in the same straight line.

(ii) ∠AOB + ∠BOC = 97° + 83° = 180°

⇒ The sum of adjacent angles AOB and BOC is 180°.

∴ The exterior arms OA and OC are in the same straight line.

(iii)∠COB + ∠AOB = 88° + 112° = 200° ; which is not 180°.

⇒ The exterior amis OA and OC are not in the same straight line.