The figure is not drawn to scale. MNQR is a parallelogram. ∠RMO is 56° and ∠QNP is 26°. MNP is an isosceles triangle and MN = NP.
- Find ∠OPN.
- Find ∠MRQ.
(a)
∠NOM = 56° (Alternate angles, MR//NQ)
∠NOP
= 180° - 56°
= 124° (Angles on a straight line)
∠OPN
= 180° - 124° - 26°
= 30° (Angles sum of triangle)
(b)
∠NMO = 30° (Isosceles triangle MNP)
∠MRQ
= 180° - 56° - 30°
= 94° (Interior angles, MN//RQ)
Answer(s): (a) 30°; (b) 94°