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 = 61° (Corresponding angles, XY//CZ)
∠CBX
= 180° - ∠ZCX - ∠CXB
= 180° - 61° - 15°
= 104° (Angles sum of triangle)
∠ABX
= 180° - 104°
= 76° (Angles on a straight line)
∠BAX = ∠ABX = 76° (Isosceles triangle)
∠i
= ∠BAX
= 76° (Corresponding angles, YZ//XA)
(b)
∠j
= 180° - 76° - 76°
= 28° (Isosceles triangle XAB)
Answer(s): (a) 76°; (b) 28°