In the figure, not drawn to scale, HJKL is a square, KLM is an equilateral triangle, KMNP is a rhombus, and JK = MK. Find
- ∠MNP
- ∠HMJ
(a)
∠LKM = 60°
∠JKM
= 90° - 60°
= 30°
KM = KJ
∠KMJ
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
∠MNP
= 180° - 75°
= 105° (Interior angles)
(b)
∠KJM = ∠KMJ = 75°
∠HJM
= 90° - 75°
= 15°
∠HMJ
= 180° - 15° - 15°
= 150° (Isosceles triangle)
Answer(s): (a) 105°; (b) 150°