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 = 63° (Corresponding angles, XY//CZ)
∠CBX
= 180° - ∠ZCX - ∠CXB
= 180° - 63° - 15°
= 102° (Angles sum of triangle)
∠ABX
= 180° - 102°
= 78° (Angles on a straight line)
∠BAX = ∠ABX = 78° (Isosceles triangle)
∠d
= ∠BAX
= 78° (Corresponding angles, YZ//XA)
(b)
∠e
= 180° - 78° - 78°
= 24° (Isosceles triangle XAB)
Answer(s): (a) 78°; (b) 24°