The figure is not drawn to scale. XYAB is a square and WXB is an equilateral triangle. YZA is an isosceles triangle. WAZ is a straight line.
- Find ∠BWA.
- Find ∠YZA.
(a)
∠ABX = 90°
∠WBX = 60° (Equilateral triangle WBB)
∠WBA
= 90° + 60°
= 150°
∠BWA
= (180° - 150°) ÷ 2
= 30° ÷ 2
= 15° (Isosceles triangle)
(b)
∠WAY
= 90° - ∠WAB;
= 90° - 15°
= 75°
∠ZAY
= 180° - ∠WAY
= 180° - 75°
= 105° (Angles on a straight line)
∠YZA
= (180° - ∠ZAC) ÷ 2
= (180° - 105°) ÷ 2
= 75° ÷ 2
= 37.5° (Isosceles triangle)
Answer(s): (a) 15°; (b) 37.5°
