Answer:
see explanation
Step-by-step explanation:
PQRS is a cyclic quadrilateral.
the opposite angles in a cyclic quadrilateral sum to 180° then
∠ Q + ∠ S = 180 ( substitute values )
3x - 8 + 3x + 8 = 180
6x = 180 ( divide both sides by 6 )
x = 30
Then
∠ Q = 3x - 8 = 3(30) - 8 = 90 - 8 = 82°
∠ S = 3x + 8 = 3(30) + 8 = 90 + 8 = 98°
∠ P = x + 15 = 30 + 15 = 45°
∠ R = 180° - ∠ P = 180° - 45° = 135°
