In triangle ABC, BE is perpendicular to AC, CD perpendicular to AB and BE and CD intersect each other at O. The bisectors of ∠OBC and ∠OCB meet at P. If ∠ BPC = 148°, then what is the measure of ∠A?
Show answer & explanation
Correct answer: D
Explanation
The correct option is 4 i.e. 64°
∠BPC = 148°
∠OBC + ∠BCO + ∠BOC = 180°
⇒ ∠BOC + 2(∠PBC + ∠PCB) = 180°
⇒ ∠BOC + 2(180° - 148°) = 180°
⇒ ∠BOC = 180 - 64 = 116°
And
∠DOE = ∠BOC = 116°
Hence,
∠A = 180 - ∠DOE = 180 - 116 = 64°