The figure is not drawn to scale. LNPQ is a trapezium and LN // QP. Given that LQ = LM, ∠QLM = 73° and ∠LNP = 100°.
- Find ∠NPQ
- Find ∠LMQ
- Find ∠MQP
(a)
∠NPQ
= 180° - 100°
= 80° (Interior angles, LN//QP)
(b)
∠LMQ
= (180° - 73°) ÷ 2
= 107° ÷ 2
= 53.5° (Isosceles triangle)
(c)
∠MQP
= ∠LMQ
= 53.5° (Alternate angles, LN//QP)
Answer(s): (a) 80°; (b) 53.5°; (c) 53.5°