PSLE In the figure, KLQR is a parallelogram and MNPQ is a rhombus. RQP is a straight line. ∠LKR = 57°, ∠QLM = 29° and ∠NMP = 32°.
- Find ∠LQM.
- Find ∠LMN.
(a)
∠LQR
= ∠LKR
= 57° (Parallelogram)
∠NPM
= ∠NMP
= 32° (Isosceles triangle)
∠MNP
= 180° - 32° - 32°
= 109° (Angles sum of triangle)
∠MQP
= ∠MNP
= 109° (Rhombus)
∠LQM
= 180° - 57° - 109°
= 14° (Angles on a straight line)
(b)
∠LMQ
= 180° - 29° - 14°
= 137° (Angles sum of triangle)
∠PMQ
= ∠NMP
= 32° (Rhombus)
∠LMN
= 360° - 137° - 32° - 32°
= 159° (Angles at a point)
Answer(s): (a) 14°; (b) 159°