In ABC, O is the point of intersection of the bisectors of ∠B and ∠A. If ∠BOC = 108°, then ∠BAO is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 18°.
∠BOC = 90° + (1/2)∠A
⇒ 108° = 90° + (1/2)∠A
⇒ (1/2)∠A = (108° - 90°) = 18°
⇒ ∠A = 36°
An angle bisector of an angle of a triangle divides the opposite side into two parts that are proportional to the other two sides of the triangle.
∠BAO = ∠A/2 = 36°/2 = 18°