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° - 138°) ÷ 2
= 42° ÷ 2
= 21° (Isosceles triangle)
∠FHJ
= 60° - 21°
= 39° (Equilateral triangle)
(b)
∠FKJ
= 60° - 21°
= 39° (Equilateral triangle)
∠FJK
= 180° - 39° - 21°
= 120° (Angles sum of triangle)
∠FJH
= 360° - 138° - 120°
= 102° (Angles at a point)
∠GFH
= ∠FHJ
= 39° (Alternate angles)
∠GFK
= 60° + 39°
= 99°
Answer(s): (a) 39°; (b) 102°; (c) 99°