The figure is not drawn to scale. NPRS is a parallelogram. ∠SNO is 58° and ∠RPQ is 25°. NPQ is an isosceles triangle and NP = PQ.
- Find ∠OQP.
- Find ∠NSR.
(a)
∠PON = 58° (Alternate angles, NS//PR)
∠POQ
= 180° - 58°
= 122° (Angles on a straight line)
∠OQP
= 180° - 122° - 25°
= 33° (Angles sum of triangle)
(b)
∠PNO = 33° (Isosceles triangle NPQ)
∠NSR
= 180° - 58° - 33°
= 89° (Interior angles, NP//SR)
Answer(s): (a) 33°; (b) 89°