In the figure, DGKN is a rectangle, KLNP is a rhombus and GHJK is a parallelogram. ∠KLN = 76° and ∠JKL = 97°.
- Find ∠FKG
- Find ∠KJH
(a)
∠NPK = ∠NLK = 76°
∠PKN
= (180° - 76°) ÷ 2
= 104° ÷ 2
= 52° (Isosceles triangle)
∠FKG
= 90° - 52°
= 38°
(b)
∠GKJ
= 360° - 97° - 90° - 52°
= 121° (Angles at a point)
∠HJK
= 180° - 121°
= 59° (Interior Angles, GK//HF)
Answer(s): (a) 38°; (b) 59°