In the figure, NPQR is a quadrilateral where ∠NPQ = 124° and ∠PQR = 112°. ∠QRS = 80° and PQ = QR. The point S on NR is such that PS is parallel to QR. Calculate
- ∠PRS
- ∠PNS
(a)
∠QRP
= (180° - 112°) ÷ 2
= 34° (Isosceles triangle)
∠PRS
= 80° - 34°
= 46°
(b)
∠PNS
= 360° - 112° - 80° - 124°
= 44° (Sum of angles in a quadrilateral)
Answer(s): (a) 46°; (b) 44°