In the figure, WZCF is a rectangle, CDFG is a rhombus and ZABC is a parallelogram. ∠CDF = 72° and ∠BCD = 96°.
- Find ∠YCZ
- Find ∠CBA
(a)
∠FGC = ∠FDC = 72°
∠GCF
= (180° - 72°) ÷ 2
= 108° ÷ 2
= 54° (Isosceles triangle)
∠YCZ
= 90° - 54°
= 36°
(b)
∠ZCB
= 360° - 96° - 90° - 54°
= 120° (Angles at a point)
∠ABC
= 180° - 120°
= 60° (Interior Angles, ZC//AF)
Answer(s): (a) 36°; (b) 60°