In the figure, not drawn to scale, JKLM is a square, LMN is an equilateral triangle, LNPQ is a rhombus, and KL = NL. Find
- ∠LQP
- ∠JNK
(a)
∠MLN = 60°
∠KLN
= 90° - 60°
= 30°
LN = LK
∠LNK
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
∠LQP
= ∠LNK
= 75° (Rhombus)
(b)
∠LKN = ∠LNK = 75°
∠JKN
= 90° - 75°
= 15°
∠JNK
= 180° - 15° - 15°
= 150° (Isosceles triangle JKN)
Answer(s): (a) 75°; (b) 150°