The figure is not drawn to scale. DEH is an equilateral triangle and GEF is an isosceles triangle. FED and EGJ are straight lines and FD//JH. ∠HEJ = 90° and ∠GHE = 53°.
- Find ∠FEJ.
- Find ∠EGF.
- Find ∠HGJ.
(a)
∠HED = 60° (Equilateral triangle DEY)
∠HEJ = 90°
∠GHE = 53°
∠FEJ
= 180° - ∠HEJ - ∠HED
= 180° - 90° - 60°
= 30° (Angles on a straight line)
(b)
∠EGF
= (180° - ∠FEJ ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(c)
∠HGE
= 180° - ∠HEJ - ∠GHE
= 180° - 90° - 53°
= 37°
∠HGJ
= 180° - ∠HGE
= 180° - 37°
= 143° (Angles on a straight line)
Answer(s): (a) 30°; (b) 75°; (c) 143°
