In the figure, XADG is a rectangle, DEGH is a rhombus and ABCD is a parallelogram. ∠DEG = 78° and ∠CDE = 95°.
- Find ∠ZDA
- Find ∠DCB
(a)
∠GHD = ∠GED = 78°
∠HDG
= (180° - 78°) ÷ 2
= 102° ÷ 2
= 51° (Isosceles triangle)
∠ZDA
= 90° - 51°
= 39°
(b)
∠ADC
= 360° - 95° - 90° - 51°
= 124° (Angles at a point)
∠BCD
= 180° - 124°
= 56° (Interior Angles, AD//BF)
Answer(s): (a) 39°; (b) 56°