PSLE In the figure, KLQR is a parallelogram and MNPQ is a rhombus. RQP is a straight line. ∠LKR = 56°, ∠QLM = 27° and ∠NMP = 34°.
- Find ∠LQM.
- Find ∠LMN.
(a)
∠LQR
= ∠LKR
= 56° (Parallelogram)
∠NPM
= ∠NMP
= 34° (Isosceles triangle)
∠MNP
= 180° - 34° - 34°
= 102° (Angles sum of triangle)
∠MQP
= ∠MNP
= 102° (Rhombus)
∠LQM
= 180° - 56° - 102°
= 22° (Angles on a straight line)
(b)
∠LMQ
= 180° - 27° - 22°
= 131° (Angles sum of triangle)
∠PMQ
= ∠NMP
= 34° (Rhombus)
∠LMN
= 360° - 131° - 34° - 34°
= 161° (Angles at a point)
Answer(s): (a) 22°; (b) 161°