In the figure, DGKN is a rectangle, KLNP is a rhombus and GHJK is a parallelogram. ∠KLN = 74° and ∠JKL = 91°.
- Find ∠FKG
- Find ∠KJH
(a)
∠NPK = ∠NLK = 74°
∠PKN
= (180° - 74°) ÷ 2
= 106° ÷ 2
= 53° (Isosceles triangle)
∠FKG
= 90° - 53°
= 37°
(b)
∠GKJ
= 360° - 91° - 90° - 53°
= 126° (Angles at a point)
∠HJK
= 180° - 126°
= 54° (Interior Angles, GK//HF)
Answer(s): (a) 37°; (b) 54°