In the figure, EHLP is a rectangle, LMPQ is a rhombus and HJKL is a parallelogram. ∠LMP = 74° and ∠KLM = 91°.
- Find ∠GLH
- Find ∠LKJ
(a)
∠PQL = ∠PML = 74°
∠QLP
= (180° - 74°) ÷ 2
= 106° ÷ 2
= 53° (Isosceles triangle)
∠GLH
= 90° - 53°
= 37°
(b)
∠HLK
= 360° - 91° - 90° - 53°
= 126° (Angles at a point)
∠JKL
= 180° - 126°
= 54° (Interior Angles, HL//JF)
Answer(s): (a) 37°; (b) 54°