The figure is not drawn to scale. MNQR is a parallelogram. ∠RMO is 58° and ∠QNP is 29°. MNP is an isosceles triangle and MN = NP.
- Find ∠OPN.
- Find ∠MRQ.
(a)
∠NOM = 58° (Alternate angles, MR//NQ)
∠NOP
= 180° - 58°
= 122° (Angles on a straight line)
∠OPN
= 180° - 122° - 29°
= 29° (Angles sum of triangle)
(b)
∠NMO = 29° (Isosceles triangle MNP)
∠MRQ
= 180° - 58° - 29°
= 93° (Interior angles, MN//RQ)
Answer(s): (a) 29°; (b) 93°