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 = 65° (Corresponding angles, XY//CZ)
∠CBX
= 180° - ∠ZCX - ∠CXB
= 180° - 65° - 17°
= 98° (Angles sum of triangle)
∠ABX
= 180° - 98°
= 82° (Angles on a straight line)
∠BAX = ∠ABX = 82° (Isosceles triangle)
∠a
= ∠BAX
= 82° (Corresponding angles, YZ//XA)
(b)
∠b
= 180° - 82° - 82°
= 16° (Isosceles triangle XAB)
Answer(s): (a) 82°; (b) 16°