The figure is not drawn to scale. GHKL is a square and FGL is an equilateral triangle. HJK is an isosceles triangle. FKJ is a straight line.
- Find ∠LFK.
- Find ∠HJK.
(a)
∠KLG = 90°
∠FLG = 60° (Equilateral triangle FLB)
∠FLK
= 90° + 60°
= 150°
∠LFK
= (180° - 150°) ÷ 2
= 30° ÷ 2
= 15° (Isosceles triangle)
(b)
∠FKH
= 90° - ∠FKL;
= 90° - 15°
= 75°
∠JKH
= 180° - ∠FKH
= 180° - 75°
= 105° (Angles on a straight line)
∠HJK
= (180° - ∠JKC) ÷ 2
= (180° - 105°) ÷ 2
= 75° ÷ 2
= 37.5° (Isosceles triangle)
Answer(s): (a) 15°; (b) 37.5°
