The figure is not drawn to scale. LMPQ is a parallelogram. ∠QLO is 56° and ∠PMN is 31°. LMN is an isosceles triangle and LM = MN.
- Find ∠ONM.
- Find ∠LQP.
(a)
∠MOL = 56° (Alternate angles, LQ//MP)
∠MON
= 180° - 56°
= 124° (Angles on a straight line)
∠ONM
= 180° - 124° - 31°
= 25° (Angles sum of triangle)
(b)
∠MLO = 25° (Isosceles triangle LMN)
∠LQP
= 180° - 56° - 25°
= 99° (Interior angles, LM//QP)
Answer(s): (a) 25°; (b) 99°