The figure is not drawn to scale. NPRS is a parallelogram. ∠SNO is 54° and ∠RPQ is 30°. NPQ is an isosceles triangle and NP = PQ.
- Find ∠OQP.
- Find ∠NSR.
(a)
∠PON = 54° (Alternate angles, NS//PR)
∠POQ
= 180° - 54°
= 126° (Angles on a straight line)
∠OQP
= 180° - 126° - 30°
= 24° (Angles sum of triangle)
(b)
∠PNO = 24° (Isosceles triangle NPQ)
∠NSR
= 180° - 54° - 24°
= 102° (Interior angles, NP//SR)
Answer(s): (a) 24°; (b) 102°