In the figure, not drawn to scale, XYZA is a square, ZAB is an equilateral triangle, ZBCD is a rhombus, and YZ = BZ. Find
- ∠ZDC
- ∠XBY
(a)
∠AZB = 60°
∠YZB
= 90° - 60°
= 30°
ZB = ZY
∠ZBY
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
∠ZDC
= ∠ZBY
= 75° (Rhombus)
(b)
∠ZYB = ∠ZBY = 75°
∠XYB
= 90° - 75°
= 15°
∠XBY
= 180° - 15° - 15°
= 150° (Isosceles triangle XYB)
Answer(s): (a) 75°; (b) 150°