Question

Quadrilateral ABCD ​ is inscribed in this circle.

What is the measure of angle A?

Answer 1

In a cyclic quadrilateral, sum of opposite angles is 180 degrees

So ∠D + ∠B = 180
⇒ x + 116 = 180
⇒ x = 180 - 116
⇒ x = 64

∠A = 2x - 40 = 2*64 - 40 = 128 - 40 = 88°

Hope it helps!

Answer 2

Hope it's help
if >B=116 then >D=116/2
x=58
>A=(2*58-40)
>A=76