Question

A kite is inscribed in a circle. Find each variable.

Answer 1

x is the same as y in this question or x=y

so as you see here in the photo both or the a's are 72° so you add them together it becomes 144°.

I'm pretty sure you've learn that you have learn that in a square, 2 opposite corners becomes 180°. To get x and y you take 180° and minus 144° leaving the value of x and y.

To basically x and y are the same value so all you gotta do is take 36° which is the after 180°-144° and divide it with 2 you get 18 which is the value of x and y.

So final answer
x=18°
y=18°
w=144°

Answer 2

∠x = (1/2) of the arc → ∠x = (1/2)(72) → ∠x = 36°
∠y = (1/2) of the arc → ∠y = (1/2)(72) → ∠y = 36°

∠y and ∠w are complimentary angles since the third angle is 90°
∠y + ∠w = 90°
36° + ∠w = 90°
         ∠w = 54°

Answer: x = 36° , y = 36° , w = 54°