PSLEFGHJ is a parallelogram, FHK is an equilateral triangle and HJ = JK.
- Find ∠FHJ.
- Find ∠HJF.
- Find ∠KFG.
(a)
HJ = JK
Triangle HJK is an isosceles triangle.
∠JHK
= (180° - 144°) ÷ 2
= 36° ÷ 2
= 18° (Isosceles triangle)
∠FHJ
= 60° - 18°
= 42° (Equilateral triangle)
(b)
∠FKJ
= 60° - 18°
= 42° (Equilateral triangle)
∠FJK
= 180° - 42° - 18°
= 120° (Angles sum of triangle)
∠FJH
= 360° - 144° - 120°
= 96° (Angles at a point)
∠GFH
= ∠FHJ
= 42° (Alternate angles)
∠GFK
= 60° + 42°
= 102°
Answer(s): (a) 42°; (b) 96°; (c) 102°