In the figure, DGKN is a rectangle, KLNP is a rhombus and GHJK is a parallelogram. ∠KLN = 80° and ∠JKL = 97°.
- Find ∠FKG
- Find ∠KJH
(a)
∠NPK = ∠NLK = 80°
∠PKN
= (180° - 80°) ÷ 2
= 100° ÷ 2
= 50° (Isosceles triangle)
∠FKG
= 90° - 50°
= 40°
(b)
∠GKJ
= 360° - 97° - 90° - 50°
= 123° (Angles at a point)
∠HJK
= 180° - 123°
= 57° (Interior Angles, GK//HF)
Answer(s): (a) 40°; (b) 57°