Question

In a quadrilateral ABCD, if AO and BO are the bisectors of ∠A and ∠B respectively, ∠C = 70° and ∠D = 30°. Then, ∠AOB = ?
(a) 40°
(b) 50°
(c) 80°
(d) 100°

Answer 1

(b) 50^o

​​Explanation:

∠C = 70^o and ∠D = 30^o
​Then ∠A + ∠B = 360^o - (70 +30)^o = 260^o
∴ $\frac{1}{2}$(∠A +∠B) =$\frac{1}{2}$ (260^o) = 130^o
In ∆​ AOB, we have:
∠AOB​ = 180^o - [$\frac{1}{2}$(∠A +∠B)​]
⇒ ∠AOB​ = ​180 - 130 = 50^o