In the figure, ADGK is a rectangle, GHKL is a rhombus and DEFG is a parallelogram. ∠GHK = 72° and ∠FGH = 96°.
- Find ∠CGD
- Find ∠GFE
(a)
∠KLG = ∠KHG = 72°
∠LGK
= (180° - 72°) ÷ 2
= 108° ÷ 2
= 54° (Isosceles triangle)
∠CGD
= 90° - 54°
= 36°
(b)
∠DGF
= 360° - 96° - 90° - 54°
= 120° (Angles at a point)
∠EFG
= 180° - 120°
= 60° (Interior Angles, DG//EF)
Answer(s): (a) 36°; (b) 60°