In the figure, not drawn to scale, ZABC is a square, BCD is an equilateral triangle, BDEF is a rhombus, and AB = DB. Find
- ∠DEF
- ∠ZDA
(a)
∠CBD = 60°
∠ABD
= 90° - 60°
= 30°
BD = BA
∠BDA
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
∠DEF
= 180° - 75°
= 105° (Interior angles)
(b)
∠BAD = ∠BDA = 75°
∠ZAD
= 90° - 75°
= 15°
∠ZDA
= 180° - 15° - 15°
= 150° (Isosceles triangle)
Answer(s): (a) 105°; (b) 150°