Question

In quadrilateral PQRS, Angle P Q R measures (7x - 2)o . Angle PSR measures (5x + 14 )o. 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 please help it's all there 15 points

Answer 1

Answer:

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Step-by-step explanation:

Fourth option is correct m Angle P Q R = 96 and m Angle P S R = 84

Therefore,

Step-by-step explanation:

Given:

In quadrilateral PQRS,

∠PQR = (7x - 2)°

∠PSR = (5x + 14)°

Circle T is inscribed with quadrilateral P Q R S.

To Find:

m∠PQR = ?

m∠PSR  = ?

Solution:

Circle T is inscribed with quadrilateral P Q R S.

Therefore,

Quadrilateral PQRS is a Cyclic Quadrilateral,

So for a Cyclic Quadrilateral, opposite Angles are Supplementary

∠PQR and ∠PSR are opposite angles

∴

Substituting the values we get

Substitute x in PQR and PSR we