PSLE In the figure, JKPQ is a parallelogram and LMNP is a rhombus. QPN is a straight line. ∠KJQ = 57°, ∠PKL = 28° and ∠MLN = 33°.
- Find ∠KPL.
- Find ∠KLM.
(a)
∠KPQ
= ∠KJQ
= 57° (Parallelogram)
∠MNL
= ∠MLN
= 33° (Isosceles triangle)
∠LMN
= 180° - 33° - 33°
= 103° (Angles sum of triangle)
∠LPN
= ∠LMN
= 103° (Rhombus)
∠KPL
= 180° - 57° - 103°
= 20° (Angles on a straight line)
(b)
∠KLP
= 180° - 28° - 20°
= 132° (Angles sum of triangle)
∠NLP
= ∠MLN
= 33° (Rhombus)
∠KLM
= 360° - 132° - 33° - 33°
= 162° (Angles at a point)
Answer(s): (a) 20°; (b) 162°