Question

6. In AABC, if ZABC = ZACB and bisectors of ZABC and ZACB intersectato, then find
the measure of ZA​

Answer 1

In ΔABC, by angle sum property we have

2x + 2y + ∠A = 180°

⇒ x + y + (∠A/2) = 90°

⇒ x + y = 90° – (∠A/2) à (1)

In ΔBOC, we have

x + y + ∠BOC = 180°

90° – (∠A/2) + ∠BOC = 180° [From (1)]

∠BOC = 180° – 90° + (∠A/2)

∠BOC = 90° + (∠A/2)