The figure is not drawn to scale. YABC is a trapezium and YA // CB. Given that YC = YZ, ∠CYZ = 75° and ∠YAB = 102°.
- Find ∠ABC
- Find ∠YZC
- Find ∠ZCB
(a)
∠ABC
= 180° - 102°
= 78° (Interior angles, YA//CB)
(b)
∠YZC
= (180° - 75°) ÷ 2
= 105° ÷ 2
= 52.5° (Isosceles triangle)
(c)
∠ZCB
= ∠YZC
= 52.5° (Alternate angles, YA//CB)
Answer(s): (a) 78°; (b) 52.5°; (c) 52.5°