In the figure, not drawn to scale, YZAB is a square, ABC is an equilateral triangle, ACDE is a rhombus, and ZA = CA. Find
- ∠CDE
- ∠YCZ
(a)
∠BAC = 60°
∠ZAC
= 90° - 60°
= 30°
AC = AZ
∠ACZ
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
∠CDE
= 180° - 75°
= 105° (Interior angles)
(b)
∠AZC = ∠ACZ = 75°
∠YZC
= 90° - 75°
= 15°
∠YCZ
= 180° - 15° - 15°
= 150° (Isosceles triangle)
Answer(s): (a) 105°; (b) 150°