The figure is not drawn to scale. YABC is a trapezium and YA // CB. Given that YC = YZ, ∠CYZ = 72° and ∠YAB = 100°.
- Find ∠ABC
- Find ∠YZC
- Find ∠ZCB
(a)
∠ABC
= 180° - 100°
= 80° (Interior angles, YA//CB)
(b)
∠YZC
= (180° - 72°) ÷ 2
= 108° ÷ 2
= 54° (Isosceles triangle)
(c)
∠ZCB
= ∠YZC
= 54° (Alternate angles, YA//CB)
Answer(s): (a) 80°; (b) 54°; (c) 54°