In the figure, ZABC is a parallelogram. BE, EF and ZA are straight lines. ZCD is an isosceles triangle.
- Find ∠y.
- Find ∠z.
(a)
∠BEZ = ∠AZF = 58° (Corresponding angles, ZA//EB)
∠EDZ
= 180° - ∠BEZ - ∠EZD
= 180° - 58° - 18°
= 104° (Angles sum of triangle)
∠CDZ
= 180° - 104°
= 76° (Angles on a straight line)
∠DCZ = ∠CDZ = 76° (Isosceles triangle)
∠y
= ∠DCZ
= 76° (Corresponding angles, AB//ZC)
(b)
∠z
= 180° - 76° - 76°
= 28° (Isosceles triangle ZCD)
Answer(s): (a) 76°; (b) 28°