The figure is not drawn to scale. NQRS is a trapezium and NQ // SR. Given that NS = NP, ∠SNP = 72° and ∠NQR = 102°.
- Find ∠QRS
- Find ∠NPS
- Find ∠PSR
(a)
∠QRS
= 180° - 102°
= 78° (Interior angles, NQ//SR)
(b)
∠NPS
= (180° - 72°) ÷ 2
= 108° ÷ 2
= 54° (Isosceles triangle)
(c)
∠PSR
= ∠NPS
= 54° (Alternate angles, NQ//SR)
Answer(s): (a) 78°; (b) 54°; (c) 54°