In the figure, XYZA is a parallelogram. ZC, CD and XY are straight lines. XAB is an isosceles triangle.
- Find ∠i.
- Find ∠j.
(a)
∠ZCX = ∠YXD = 65° (Corresponding angles, XY//CZ)
∠CBX
= 180° - ∠ZCX - ∠CXB
= 180° - 65° - 19°
= 96° (Angles sum of triangle)
∠ABX
= 180° - 96°
= 84° (Angles on a straight line)
∠BAX = ∠ABX = 84° (Isosceles triangle)
∠i
= ∠BAX
= 84° (Corresponding angles, YZ//XA)
(b)
∠j
= 180° - 84° - 84°
= 12° (Isosceles triangle XAB)
Answer(s): (a) 84°; (b) 12°