In the figure, XYZA is a parallelogram. ZC, CD and XY are straight lines. XAB is an isosceles triangle.
- Find ∠d.
- Find ∠e.
(a)
∠ZCX = ∠YXD = 64° (Corresponding angles, XY//CZ)
∠CBX
= 180° - ∠ZCX - ∠CXB
= 180° - 64° - 17°
= 99° (Angles sum of triangle)
∠ABX
= 180° - 99°
= 81° (Angles on a straight line)
∠BAX = ∠ABX = 81° (Isosceles triangle)
∠d
= ∠BAX
= 81° (Corresponding angles, YZ//XA)
(b)
∠e
= 180° - 81° - 81°
= 18° (Isosceles triangle XAB)
Answer(s): (a) 81°; (b) 18°