In the figure, EHLP is a rectangle, LMPQ is a rhombus and HJKL is a parallelogram. ∠LMP = 72° and ∠KLM = 92°.
- Find ∠GLH
- Find ∠LKJ
(a)
∠PQL = ∠PML = 72°
∠QLP
= (180° - 72°) ÷ 2
= 108° ÷ 2
= 54° (Isosceles triangle)
∠GLH
= 90° - 54°
= 36°
(b)
∠HLK
= 360° - 92° - 90° - 54°
= 124° (Angles at a point)
∠JKL
= 180° - 124°
= 56° (Interior Angles, HL//JF)
Answer(s): (a) 36°; (b) 56°