The figure is not drawn to scale. NPRS is a parallelogram. ∠SNO is 60° and ∠RPQ is 31°. NPQ is an isosceles triangle and NP = PQ.
- Find ∠OQP.
- Find ∠NSR.
(a)
∠PON = 60° (Alternate angles, NS//PR)
∠POQ
= 180° - 60°
= 120° (Angles on a straight line)
∠OQP
= 180° - 120° - 31°
= 29° (Angles sum of triangle)
(b)
∠PNO = 29° (Isosceles triangle NPQ)
∠NSR
= 180° - 60° - 29°
= 91° (Interior angles, NP//SR)
Answer(s): (a) 29°; (b) 91°