PSLECDEF is a parallelogram, CEG is an equilateral triangle and EF = FG.
- Find ∠CEF.
- Find ∠EFC.
- Find ∠GCD.
(a)
EF = FG
Triangle EFG is an isosceles triangle.
∠FEG
= (180° - 138°) ÷ 2
= 42° ÷ 2
= 21° (Isosceles triangle)
∠CEF
= 60° - 21°
= 39° (Equilateral triangle)
(b)
∠CGF
= 60° - 21°
= 39° (Equilateral triangle)
∠CFG
= 180° - 39° - 21°
= 120° (Angles sum of triangle)
∠CFE
= 360° - 138° - 120°
= 102° (Angles at a point)
∠DCE
= ∠CEF
= 39° (Alternate angles)
∠DCG
= 60° + 39°
= 99°
Answer(s): (a) 39°; (b) 102°; (c) 99°