ΔABC is isosceles having AB = AC and ∠A = 40°. Bisectors PO and OQ of the exterior angles ∠ABD and ∠ACE formed by producing BC on both sides, meet at O. Then the value of ∠BOC is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1
In ΔABC:
40 + x + x = 180°
⇒ x = 70°
∠PBD = ∠OBC = 1/2 (180 - 70) = 55°
In ΔOBC:
∠BOC + ∠OBC + ∠OCB = 180°
⇒ ∠BOC + 110° = 180°
⇒ ∠BOC = 70°