In the figure, XYZA is a parallelogram. ZC, CD and XY are straight lines. XAB is an isosceles triangle.
- Find ∠c.
- Find ∠d.
(a)
∠ZCX = ∠YXD = 59° (Corresponding angles, XY//CZ)
∠CBX
= 180° - ∠ZCX - ∠CXB
= 180° - 59° - 16°
= 105° (Angles sum of triangle)
∠ABX
= 180° - 105°
= 75° (Angles on a straight line)
∠BAX = ∠ABX = 75° (Isosceles triangle)
∠c
= ∠BAX
= 75° (Corresponding angles, YZ//XA)
(b)
∠d
= 180° - 75° - 75°
= 30° (Isosceles triangle XAB)
Answer(s): (a) 75°; (b) 30°