PSLE In the figure, MNPQ is a parallelogram. KQM and LQP are straight lines and KL = LM. ∠KLQ = 30° and ∠NPQ = 57°.
- Find ∠PQM.
- Find ∠QLM.
(a)
∠PQM
= 180° - 57°
= 123° (Interior angles)
(b)
∠KQL
= ∠PQM
= 123° (Vertically opposite angles)
∠LKQ
= 180° - 123° - 30°
= 27° (Angles sum of triangle)
∠LMQ = ∠LKQ (Isosceles triangle)
∠KLM
= 180° - 27° - 27°
= 126° (Angles sum of triangle)
∠QLM
= 126° - 30°
= 96°
Answer(s): (a) 123°; (b) 96°