The figure is not drawn to scale. LMPQ is a parallelogram. ∠QLO is 59° and ∠PMN is 25°. LMN is an isosceles triangle and LM = MN.
- Find ∠ONM.
- Find ∠LQP.
(a)
∠MOL = 59° (Alternate angles, LQ//MP)
∠MON
= 180° - 59°
= 121° (Angles on a straight line)
∠ONM
= 180° - 121° - 25°
= 34° (Angles sum of triangle)
(b)
∠MLO = 34° (Isosceles triangle LMN)
∠LQP
= 180° - 59° - 34°
= 87° (Interior angles, LM//QP)
Answer(s): (a) 34°; (b) 87°