In quadrilateral PQRS, Angle P Q R measures (7x - 2)°. Angle PSR measures (5x + 14)°. What are the measures of angles PQR and PSR?

Solution:

Given,

In quadrilateral PQRS,

∠PQR = (7X - 2)°

∠PSR = (5X +14)°

Quadrilateral PQRS is a cyclic quadrilateral.

So, opposite angles are supplementary.

∠PQR and ∠PSR are opposite angles.

m∠PQR + m∠PSR = 180°

 (7X - 2)° + (5X + 14)° = 180

12x + 12 = 180

12x = 180 - 12

12x = 168

X = 168/12

X = 14

Substituting x in PQR and PSR, we get

m∠PQR = 7(14) - 2 = 96°

m∠PSR = 5(14) + 14 = 84 °

Therefore, the measures of angles PQR and PSR are 96° and 84 ° respectively.

In quadrilateral PQRS, Angle P Q R measures (7x - 2)°. Angle PSR measures (5x + 14)°. What are the measures of angles PQR and PSR?

Summary:

In quadrilateral PQRS, Angle P Q R measures (7x - 2)°. Angle PSR measures (5x + 14)°. The measures of angles PQR and PSR are 96° and 84 ° respectively.