The figure is not drawn to scale. NPRS is a parallelogram. ∠SNO is 57° and ∠RPQ is 26°. NPQ is an isosceles triangle and NP = PQ.
- Find ∠OQP.
- Find ∠NSR.
(a)
∠PON = 57° (Alternate angles, NS//PR)
∠POQ
= 180° - 57°
= 123° (Angles on a straight line)
∠OQP
= 180° - 123° - 26°
= 31° (Angles sum of triangle)
(b)
∠PNO = 31° (Isosceles triangle NPQ)
∠NSR
= 180° - 57° - 31°
= 92° (Interior angles, NP//SR)
Answer(s): (a) 31°; (b) 92°