The figure is not drawn to scale. LMPQ is a parallelogram. ∠QLO is 54° and ∠PMN is 30°. LMN is an isosceles triangle and LM = MN.
- Find ∠ONM.
- Find ∠LQP.
(a)
∠MOL = 54° (Alternate angles, LQ//MP)
∠MON
= 180° - 54°
= 126° (Angles on a straight line)
∠ONM
= 180° - 126° - 30°
= 24° (Angles sum of triangle)
(b)
∠MLO = 24° (Isosceles triangle LMN)
∠LQP
= 180° - 54° - 24°
= 102° (Interior angles, LM//QP)
Answer(s): (a) 24°; (b) 102°