The figure is not drawn to scale. NQRS is a trapezium and NQ // SR. Given that NS = NP, ∠SNP = 73° and ∠NQR = 101°.
- Find ∠QRS
- Find ∠NPS
- Find ∠PSR
(a)
∠QRS
= 180° - 101°
= 79° (Interior angles, NQ//SR)
(b)
∠NPS
= (180° - 73°) ÷ 2
= 107° ÷ 2
= 53.5° (Isosceles triangle)
(c)
∠PSR
= ∠NPS
= 53.5° (Alternate angles, NQ//SR)
Answer(s): (a) 79°; (b) 53.5°; (c) 53.5°