The figure is not drawn to scale. ABDE is a square and ZAE is an equilateral triangle. BCD is an isosceles triangle. ZDC is a straight line.
- Find ∠EZD.
- Find ∠BCD.
(a)
∠DEA = 90°
∠ZEA = 60° (Equilateral triangle ZEB)
∠ZED
= 90° + 60°
= 150°
∠EZD
= (180° - 150°) ÷ 2
= 30° ÷ 2
= 15° (Isosceles triangle)
(b)
∠ZDB
= 90° - ∠ZDE;
= 90° - 15°
= 75°
∠CDB
= 180° - ∠ZDB
= 180° - 75°
= 105° (Angles on a straight line)
∠BCD
= (180° - ∠CDC) ÷ 2
= (180° - 105°) ÷ 2
= 75° ÷ 2
= 37.5° (Isosceles triangle)
Answer(s): (a) 15°; (b) 37.5°
