In the figure, YZAB is a parallelogram. AD, DE and YZ are straight lines. YBC is an isosceles triangle.
- Find ∠x.
- Find ∠y.
(a)
∠ADY = ∠ZYE = 59° (Corresponding angles, YZ//DA)
∠DCY
= 180° - ∠ADY - ∠DYC
= 180° - 59° - 15°
= 106° (Angles sum of triangle)
∠BCY
= 180° - 106°
= 74° (Angles on a straight line)
∠CBY = ∠BCY = 74° (Isosceles triangle)
∠x
= ∠CBY
= 74° (Corresponding angles, ZA//YB)
(b)
∠y
= 180° - 74° - 74°
= 32° (Isosceles triangle YBC)
Answer(s): (a) 74°; (b) 32°
