Question

In a cyclic quadrilateral abcd , if angle a +angle b = 185 and angle b+angle c = 165 find angle d

Answer 1

∠A + ∠B = 185°

∠A = 185 - ∠B

∠B + ∠C = 165°

∠C = 165 - ∠B

In cyclic quadrilateral opposite angles are supplementary.

=> ∠A + ∠C = 180

185 - ∠B + 165 - ∠B = 180

-2B + 350 = 180

-2∠B = 180 - 350

-2∠B = -170

∠B = -170/-2

∠B = 85°

In cyclic quadrilateral opposite angles are supplementary.

∠B + ∠D = 180

85 + ∠D = 180

∠D = 180 - 85

∠D = 95°