The figure is not drawn to scale. YABC is a trapezium and YA // CB. Given that YC = YZ, ∠CYZ = 74° and ∠YAB = 103°.
- Find ∠ABC
- Find ∠YZC
- Find ∠ZCB
(a)
∠ABC
= 180° - 103°
= 77° (Interior angles, YA//CB)
(b)
∠YZC
= (180° - 74°) ÷ 2
= 106° ÷ 2
= 53° (Isosceles triangle)
(c)
∠ZCB
= ∠YZC
= 53° (Alternate angles, YA//CB)
Answer(s): (a) 77°; (b) 53°; (c) 53°