In the figure, not drawn to scale, LMNP is a square, NPQ is an equilateral triangle, NQRS is a rhombus, and MN = QN. Find
- ∠QRS
- ∠LQM
(a)
∠PNQ = 60°
∠MNQ
= 90° - 60°
= 30°
NQ = NM
∠NQM
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
∠QRS
= 180° - 75°
= 105° (Interior angles)
(b)
∠NMQ = ∠NQM = 75°
∠LMQ
= 90° - 75°
= 15°
∠LQM
= 180° - 15° - 15°
= 150° (Isosceles triangle)
Answer(s): (a) 105°; (b) 150°