In the figure, YZAB is a parallelogram. AD, DE and YZ are straight lines. YBC is an isosceles triangle.
- Find ∠q.
- Find ∠r.
(a)
∠ADY = ∠ZYE = 63° (Corresponding angles, YZ//DA)
∠DCY
= 180° - ∠ADY - ∠DYC
= 180° - 63° - 21°
= 96° (Angles sum of triangle)
∠BCY
= 180° - 96°
= 84° (Angles on a straight line)
∠CBY = ∠BCY = 84° (Isosceles triangle)
∠q
= ∠CBY
= 84° (Corresponding angles, ZA//YB)
(b)
∠r
= 180° - 84° - 84°
= 12° (Isosceles triangle YBC)
Answer(s): (a) 84°; (b) 12°