In the figure, not drawn to scale, GHJK is a square, JKL is an equilateral triangle, JLMN is a rhombus, and HJ = LJ. Find
- ∠LMN
- ∠GLH
(a)
∠KJL = 60°
∠HJL
= 90° - 60°
= 30°
JL = JH
∠JLH
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
∠LMN
= 180° - 75°
= 105° (Interior angles)
(b)
∠JHL = ∠JLH = 75°
∠GHL
= 90° - 75°
= 15°
∠GLH
= 180° - 15° - 15°
= 150° (Isosceles triangle)
Answer(s): (a) 105°; (b) 150°