In the figure, WZCF is a rectangle, CDFG is a rhombus and ZABC is a parallelogram. ∠CDF = 74° and ∠BCD = 92°.
- Find ∠YCZ
- Find ∠CBA
(a)
∠FGC = ∠FDC = 74°
∠GCF
= (180° - 74°) ÷ 2
= 106° ÷ 2
= 53° (Isosceles triangle)
∠YCZ
= 90° - 53°
= 37°
(b)
∠ZCB
= 360° - 92° - 90° - 53°
= 125° (Angles at a point)
∠ABC
= 180° - 125°
= 55° (Interior Angles, ZC//AF)
Answer(s): (a) 37°; (b) 55°