The figure is not drawn to scale. NPRS is a parallelogram. ∠SNO is 56° and ∠RPQ is 28°. NPQ is an isosceles triangle and NP = PQ.
- Find ∠OQP.
- Find ∠NSR.
(a)
∠PON = 56° (Alternate angles, NS//PR)
∠POQ
= 180° - 56°
= 124° (Angles on a straight line)
∠OQP
= 180° - 124° - 28°
= 28° (Angles sum of triangle)
(b)
∠PNO = 28° (Isosceles triangle NPQ)
∠NSR
= 180° - 56° - 28°
= 96° (Interior angles, NP//SR)
Answer(s): (a) 28°; (b) 96°