Question

Find the measure of ∠B if ∠A = 5 2 x + 40 ∠B = 7 2 x + 20 ∠C = 3 2 x + 20 ∠D = 3 2 x + 40

Answer 1

In a quadrilateral
∠A = 52 x + 40
∠B = 72 x + 20
∠C = 32 x + 20
∠D = 32 x + 40
∠A +∠B +∠C +∠D = 360° = 52x+40+72x+20+32x+20+32x+40
= 188x + 120
188x +120 = 360°
188x =240°
x= 240/188 =1.27°
∠B = 72x+20= (72×1.27)+20 =111.44°

Answer 2

104°

Opposite angles in a cyclic quadrilateral are supplementary.

7/2x + 20 +  3/2x + 40 = 180

x = 24

∠B =  7/2x + 20

∠B =  7/2(24) + 20 = 104