The figure is not drawn to scale. WXZA is a square and VWA is an equilateral triangle. XYZ is an isosceles triangle. VZY is a straight line.
- Find ∠AVZ.
- Find ∠XYZ.
(a)
∠ZAW = 90°
∠VAW = 60° (Equilateral triangle VAB)
∠VAZ
= 90° + 60°
= 150°
∠AVZ
= (180° - 150°) ÷ 2
= 30° ÷ 2
= 15° (Isosceles triangle)
(b)
∠VZX
= 90° - ∠VZA;
= 90° - 15°
= 75°
∠YZX
= 180° - ∠VZX
= 180° - 75°
= 105° (Angles on a straight line)
∠XYZ
= (180° - ∠YZC) ÷ 2
= (180° - 105°) ÷ 2
= 75° ÷ 2
= 37.5° (Isosceles triangle)
Answer(s): (a) 15°; (b) 37.5°
