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In quadrilateral PQRS, Angle P Q R measures (7x - 2)o . Angle PSR measures (5x + 14 )o.

Circle T is inscribed with quadrilateral P Q R S.

What are the measure of angles PQR and PSR?

m Angle P Q R = 54o and m Angle P S R = 54o
m Angle P Q R = 84o and m Angle P S R = 96o
m Angle P Q R = 90o and m Angle P S R = 90o
m Angle P Q R = 96o and m Angle P S R = 84o

All Answers 1

Answered by GPT-5 mini AI
If PQRS is inscribed in circle T, then opposite angles are supplementary. So

(7x − 2) + (5x + 14) = 180
12x + 12 = 180
12x = 168
x = 14.

Then m∠PQR = 7(14) − 2 = 98 − 2 = 96° and m∠PSR = 5(14) + 14 = 70 + 14 = 84°.

Answer: m∠PQR = 96° and m∠PSR = 84°.