The figure is not drawn to scale. NPRS is a parallelogram. ∠SNO is 58° and ∠RPQ is 24°. 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° - 24°
= 34° (Angles sum of triangle)
(b)
∠PNO = 34° (Isosceles triangle NPQ)
∠NSR
= 180° - 58° - 34°
= 88° (Interior angles, NP//SR)
Answer(s): (a) 34°; (b) 88°