WXYZ is a square. FEY and XEZ are straight lines. XW = XF and ∠EXF = 15°. Find
- ∠XWF
- ∠ZYF
.
(a)
∠WXZ = 45° (Right angle)
∠WXF
= ∠WXZ - ∠EXF
= 45° - 15°
= 30°
∠XWF
= (180° - ∠WXF) ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(b)
XW = XF = XY
FXY is an isosceles triangle.
∠XFY = ∠XYF (Isosceles triangle)
∠XYF
= (180° - ∠ZXY - ∠EXF) ÷ 2
= (180° - 45° -15°) ÷ 2
= 120° ÷ 2
= 60°
∠ZYF
= ∠XYZ - ∠XYF
= 90° - 60°
= 30°
Answer(s): (a) 75°; (b) 30°
