In the figure, not drawn to scale, KLMN is a square, MNP is an equilateral triangle, MPQR is a rhombus, and LM = PM. Find
- ∠PQR
- ∠KPL
(a)
∠NMP = 60°
∠LMP
= 90° - 60°
= 30°
MP = ML
∠MPL
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
∠PQR
= 180° - 75°
= 105° (Interior angles)
(b)
∠MLP = ∠MPL = 75°
∠KLP
= 90° - 75°
= 15°
∠KPL
= 180° - 15° - 15°
= 150° (Isosceles triangle)
Answer(s): (a) 105°; (b) 150°