In the figure, ADGK is a rectangle, GHKL is a rhombus and DEFG is a parallelogram. ∠GHK = 76° and ∠FGH = 96°.
- Find ∠CGD
- Find ∠GFE
(a)
∠KLG = ∠KHG = 76°
∠LGK
= (180° - 76°) ÷ 2
= 104° ÷ 2
= 52° (Isosceles triangle)
∠CGD
= 90° - 52°
= 38°
(b)
∠DGF
= 360° - 96° - 90° - 52°
= 122° (Angles at a point)
∠EFG
= 180° - 122°
= 58° (Interior Angles, DG//EF)
Answer(s): (a) 38°; (b) 58°