The figure is not drawn to scale. LMPQ is a parallelogram. ∠QLO is 58° and ∠PMN is 27°. LMN is an isosceles triangle and LM = MN.
- Find ∠ONM.
- Find ∠LQP.
(a)
∠MOL = 58° (Alternate angles, LQ//MP)
∠MON
= 180° - 58°
= 122° (Angles on a straight line)
∠ONM
= 180° - 122° - 27°
= 31° (Angles sum of triangle)
(b)
∠MLO = 31° (Isosceles triangle LMN)
∠LQP
= 180° - 58° - 31°
= 91° (Interior angles, LM//QP)
Answer(s): (a) 31°; (b) 91°