PSLE In the figure, JKPQ is a parallelogram and LMNP is a rhombus. QPN is a straight line. ∠KJQ = 56°, ∠PKL = 29° and ∠MLN = 32°.
- Find ∠KPL.
- Find ∠KLM.
(a)
∠KPQ
= ∠KJQ
= 56° (Parallelogram)
∠MNL
= ∠MLN
= 32° (Isosceles triangle)
∠LMN
= 180° - 32° - 32°
= 106° (Angles sum of triangle)
∠LPN
= ∠LMN
= 106° (Rhombus)
∠KPL
= 180° - 56° - 106°
= 18° (Angles on a straight line)
(b)
∠KLP
= 180° - 29° - 18°
= 133° (Angles sum of triangle)
∠NLP
= ∠MLN
= 32° (Rhombus)
∠KLM
= 360° - 133° - 32° - 32°
= 163° (Angles at a point)
Answer(s): (a) 18°; (b) 163°