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Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the Quadrilateral. Show your work. ( Please do not repaste another students answer on brianly or another other websites). Only answer if your 100% correct and you'll get Brainliest . ​

Quadrilateral ABCD is inscribed in a circle Find the measure of each of the angles of the Quadrilateral Show your work Please do not repaste another students an class=

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Answer:

A = 92°

B = 100°

C = 88°

D = 80°

Step-by-step explanation:

Cyclic quadrilateral : a quadrilateral drawn inside (inscribed) a circle.

The opposite angles in a cyclic quadrilateral add up to 180°.

Therefore, A + C = 180° and B + D = 180°

If A + C = 180° , then

⇒ (x + 2) + (x - 2) = 180

⇒ x + 2 + x - 2 = 180

⇒ 2x = 180

⇒ x = 90°

Therefore,

A = x + 2 = 90 + 2 = 92°

C = x - 2 = 90 - 2 = 88°

D = x - 10 = 90 - 10 = 80°

B = 180 - D = 180 - 80 = 100°

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