The figure is not drawn to scale. LNPQ is a trapezium and LN // QP. Given that LQ = LM, ∠QLM = 74° and ∠LNP = 102°.
- Find ∠NPQ
- Find ∠LMQ
- Find ∠MQP
(a)
∠NPQ
= 180° - 102°
= 78° (Interior angles, LN//QP)
(b)
∠LMQ
= (180° - 74°) ÷ 2
= 106° ÷ 2
= 53° (Isosceles triangle)
(c)
∠MQP
= ∠LMQ
= 53° (Alternate angles, LN//QP)
Answer(s): (a) 78°; (b) 53°; (c) 53°