In the figure, XYZA is a parallelogram. ZC, CD and XY are straight lines. XAB is an isosceles triangle.
- Find ∠x.
- Find ∠y.
(a)
∠ZCX = ∠YXD = 66° (Corresponding angles, XY//CZ)
∠CBX
= 180° - ∠ZCX - ∠CXB
= 180° - 66° - 17°
= 97° (Angles sum of triangle)
∠ABX
= 180° - 97°
= 83° (Angles on a straight line)
∠BAX = ∠ABX = 83° (Isosceles triangle)
∠x
= ∠BAX
= 83° (Corresponding angles, YZ//XA)
(b)
∠y
= 180° - 83° - 83°
= 14° (Isosceles triangle XAB)
Answer(s): (a) 83°; (b) 14°