The figure is not drawn to scale. MNQR is a parallelogram. ∠RMO is 57° and ∠QNP is 25°. MNP is an isosceles triangle and MN = NP.
- Find ∠OPN.
- Find ∠MRQ.
(a)
∠NOM = 57° (Alternate angles, MR//NQ)
∠NOP
= 180° - 57°
= 123° (Angles on a straight line)
∠OPN
= 180° - 123° - 25°
= 32° (Angles sum of triangle)
(b)
∠NMO = 32° (Isosceles triangle MNP)
∠MRQ
= 180° - 57° - 32°
= 91° (Interior angles, MN//RQ)
Answer(s): (a) 32°; (b) 91°