Answer:
∠ RPQ = 28°
Step-by-step explanation:
Since PS = PQ then Δ SPQ is isosceles and the base angles are congruent.
∠ SPQ = ∠ SQP = x
Thus ∠ RQP = ∠ SQR + ∠ SQP = 34 + x
The sum of the 3 angles in Δ RPQ = 180°, thus
x + x + 34 + 90 = 180
2x + 124 = 180 ( subtract 124 from both sides )
2x = 56 ( divide both sides by 2 )
x = 28
Thus
∠ RPQ = x = 28°
