In the figure, XYZA is a parallelogram. ZC, CD and XY are straight lines. XAB is an isosceles triangle.
- Find ∠a.
- Find ∠b.
(a)
∠ZCX = ∠YXD = 63° (Corresponding angles, XY//CZ)
∠CBX
= 180° - ∠ZCX - ∠CXB
= 180° - 63° - 16°
= 101° (Angles sum of triangle)
∠ABX
= 180° - 101°
= 79° (Angles on a straight line)
∠BAX = ∠ABX = 79° (Isosceles triangle)
∠a
= ∠BAX
= 79° (Corresponding angles, YZ//XA)
(b)
∠b
= 180° - 79° - 79°
= 22° (Isosceles triangle XAB)
Answer(s): (a) 79°; (b) 22°