In the figure, not drawn to scale, WXYZ is a square, YZA is an equilateral triangle, YABC is a rhombus, and XY = AY. Find
- ∠ABC
- ∠WAX
(a)
∠ZYA = 60°
∠XYA
= 90° - 60°
= 30°
YA = YX
∠YAX
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
∠ABC
= 180° - 75°
= 105° (Interior angles)
(b)
∠YXA = ∠YAX = 75°
∠WXA
= 90° - 75°
= 15°
∠WAX
= 180° - 15° - 15°
= 150° (Isosceles triangle)
Answer(s): (a) 105°; (b) 150°