WXYZ is a square. TSY and XSZ are straight lines. XW = XT and ∠SXT = 15°. Find
- ∠XWT
- ∠ZYT
.
(a)
∠WXZ = 45° (Right angle)
∠WXT
= ∠WXZ - ∠SXT
= 45° - 15°
= 30°
∠XWT
= (180° - ∠WXT) ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(b)
XW = XT = XY
TXY is an isosceles triangle.
∠XTY = ∠XYT (Isosceles triangle)
∠XYT
= (180° - ∠ZXY - ∠SXT) ÷ 2
= (180° - 45° -15°) ÷ 2
= 120° ÷ 2
= 60°
∠ZYT
= ∠XYZ - ∠XYT
= 90° - 60°
= 30°
Answer(s): (a) 75°; (b) 30°
