In the figure, NPQR is a quadrilateral where ∠NPQ = 131° and ∠PQR = 120°. ∠QRS = 75° and PQ = QR. The point S on NR is such that PS is parallel to QR. Calculate
- ∠PRS
- ∠PNS
(a)
∠QRP
= (180° - 120°) ÷ 2
= 30° (Isosceles triangle)
∠PRS
= 75° - 30°
= 45°
(b)
∠PNS
= 360° - 120° - 75° - 131°
= 34° (Sum of angles in a quadrilateral)
Answer(s): (a) 45°; (b) 34°