In the figure, YZAB is a parallelogram. AD, DE and YZ are straight lines. YBC is an isosceles triangle.
- Find ∠t.
- Find ∠v.
(a)
∠ADY = ∠ZYE = 58° (Corresponding angles, YZ//DA)
∠DCY
= 180° - ∠ADY - ∠DYC
= 180° - 58° - 17°
= 105° (Angles sum of triangle)
∠BCY
= 180° - 105°
= 75° (Angles on a straight line)
∠CBY = ∠BCY = 75° (Isosceles triangle)
∠t
= ∠CBY
= 75° (Corresponding angles, ZA//YB)
(b)
∠v
= 180° - 75° - 75°
= 30° (Isosceles triangle YBC)
Answer(s): (a) 75°; (b) 30°