Question

2. Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.

Answer 1

Ans: 
1. m ∠C = 88°
2. m ∠B = 100°
3. m ∠A = 92°
4. m ∠D = 80°

Explanation:
∠A and ∠C are supplementary angles; therefore:
∠A + ∠C = 180° --- (A)

Since,
∠A = (x+2)°
and
∠C = (x-2)°

Plug-in the values in equation (A):
(A) => (x+2)° + (x-2)° = 180°
=> x° + 2° + x° - 2° = 180°
=> 2x° = 180°
=> x = 90°

Since x = 90°, therefore,
∠A = (x+2)° = 92°,
and
∠C = (x-2)° = 88°

Since ∠B and ∠D are supplementary angles; therefore,
∠B + ∠D = 180°
∠B + (x-10)° = 180°

Since,
x = 90°; therefore,

∠B + 80° = 180°
∠B = 100°

And since,
∠B + ∠D = 180°
and
∠B = 100°

Therefore,

∠D = 180° - 100°
∠D= 80°

-i