The figure is not drawn to scale. KLNP is a square and JKP is an equilateral triangle. LMN is an isosceles triangle. JNM is a straight line.
- Find ∠PJN.
- Find ∠LMN.
(a)
∠NPK = 90°
∠JPK = 60° (Equilateral triangle JPB)
∠JPN
= 90° + 60°
= 150°
∠PJN
= (180° - 150°) ÷ 2
= 30° ÷ 2
= 15° (Isosceles triangle)
(b)
∠JNL
= 90° - ∠JNP;
= 90° - 15°
= 75°
∠MNL
= 180° - ∠JNL
= 180° - 75°
= 105° (Angles on a straight line)
∠LMN
= (180° - ∠MNC) ÷ 2
= (180° - 105°) ÷ 2
= 75° ÷ 2
= 37.5° (Isosceles triangle)
Answer(s): (a) 15°; (b) 37.5°
