The figure is not drawn to scale. JKMN is a square and HJN is an equilateral triangle. KLM is an isosceles triangle. HML is a straight line.
- Find ∠NHM.
- Find ∠KLM.
(a)
∠MNJ = 90°
∠HNJ = 60° (Equilateral triangle HNB)
∠HNM
= 90° + 60°
= 150°
∠NHM
= (180° - 150°) ÷ 2
= 30° ÷ 2
= 15° (Isosceles triangle)
(b)
∠HMK
= 90° - ∠HMN;
= 90° - 15°
= 75°
∠LMK
= 180° - ∠HMK
= 180° - 75°
= 105° (Angles on a straight line)
∠KLM
= (180° - ∠LMC) ÷ 2
= (180° - 105°) ÷ 2
= 75° ÷ 2
= 37.5° (Isosceles triangle)
Answer(s): (a) 15°; (b) 37.5°
