Question

In a cyclic quadrilateral ABCD, it is being given that ∠A = (x + y + 10)°, ∠B = (y + 20)°, ∠C = (x + y – 30)° and ∠D = (x + y)°. Then, ∠B = ?

पर्याय

• 70°

• 80°

• 100°

• 110°

Answer 1

80°

Explanation:

In a cyclic quadrilateral, opposite angles are supplementary and sum to 180°. 

So, A + C = 180°: (x + y + 10) + (x + y – 30) = 180° 

⇒ 2(x + y) – 20 = 180° 

⇒ x + y = 100°

Thus, D = x + y = 100° and B + D = 180°

⇒ B = 180° – 100° 

= 80°