The figure is not drawn to scale. MNQR is a parallelogram. ∠RMO is 54° and ∠QNP is 25°. MNP is an isosceles triangle and MN = NP.
- Find ∠OPN.
- Find ∠MRQ.
(a)
∠NOM = 54° (Alternate angles, MR//NQ)
∠NOP
= 180° - 54°
= 126° (Angles on a straight line)
∠OPN
= 180° - 126° - 25°
= 29° (Angles sum of triangle)
(b)
∠NMO = 29° (Isosceles triangle MNP)
∠MRQ
= 180° - 54° - 29°
= 97° (Interior angles, MN//RQ)
Answer(s): (a) 29°; (b) 97°