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° - 134°) ÷ 2
= 46° ÷ 2
= 23° (Isosceles triangle)
∠FHJ
= 60° - 23°
= 37° (Equilateral triangle)
(b)
∠FKJ
= 60° - 23°
= 37° (Equilateral triangle)
∠FJK
= 180° - 37° - 23°
= 120° (Angles sum of triangle)
∠FJH
= 360° - 134° - 120°
= 106° (Angles at a point)
∠GFH
= ∠FHJ
= 37° (Alternate angles)
∠GFK
= 60° + 37°
= 97°
Answer(s): (a) 37°; (b) 106°; (c) 97°