Answer:
∠ RPQ = 28°
Step-by-step explanation:
Given ∠ PRQ = 90° and ∠ SQR = 34°
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ PSQ is an exterior angle of the triangle, so
∠ PSQ = 90° + 34° = 124°
Since PS = SQ then Δ PQS is isosceles and then base angles are congruent
∠ SPQ = ∠ SQP , thus
∠ RPQ = [tex]\frac{180-124}{2}[/tex] = [tex]\frac{56}{2}[/tex] = 28°
