The figure is not drawn to scale. FGJK is a square and EFK is an equilateral triangle. GHJ is an isosceles triangle. EJH is a straight line.
- Find ∠KEJ.
- Find ∠GHJ.
(a)
∠JKF = 90°
∠EKF = 60° (Equilateral triangle EKB)
∠EKJ
= 90° + 60°
= 150°
∠KEJ
= (180° - 150°) ÷ 2
= 30° ÷ 2
= 15° (Isosceles triangle)
(b)
∠EJG
= 90° - ∠EJK;
= 90° - 15°
= 75°
∠HJG
= 180° - ∠EJG
= 180° - 75°
= 105° (Angles on a straight line)
∠GHJ
= (180° - ∠HJC) ÷ 2
= (180° - 105°) ÷ 2
= 75° ÷ 2
= 37.5° (Isosceles triangle)
Answer(s): (a) 15°; (b) 37.5°
