Quadrilateral OPQR is inscribed inside a circle as shown below. What is the measure of angle Q? You must show all work and calcu

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2 years ago

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1 answer:

Firlakuza [10] · Answer 1 · 2023-04-08T15:46:52+03:00

Answer:

the measure of angle Q = 92°

Step-by-step explanation:

<u><em>The quadrilateral OPQR is inscribed inside a circle, then its opposite angles are supplementary</em></u>.

………………………………

Then

m∠O + m∠Q = 180

Then

2x + (2x+4) = 180

Then

4x + 4 = 180

Then

4x = 180 - 4

Then

4x = 176

Then

x = 176/4

Then

x = 44

Therefore

m∠Q = 2(44) + 4 = 88 + 4 = 92°