VWXY is a square. DCX and WCY are straight lines. WV = WD and ∠CWD = 15°. Find
- ∠WVD
- ∠YXD
.
(a)
∠VWY = 45° (Right angle)
∠VWD
= ∠VWY - ∠CWD
= 45° - 15°
= 30°
∠WVD
= (180° - ∠VWD) ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(b)
WV = WD = WX
DWX is an isosceles triangle.
∠WDX = ∠WXD (Isosceles triangle)
∠WXD
= (180° - ∠YWX - ∠CWD) ÷ 2
= (180° - 45° -15°) ÷ 2
= 120° ÷ 2
= 60°
∠YXD
= ∠WXY - ∠WXD
= 90° - 60°
= 30°
Answer(s): (a) 75°; (b) 30°
