In the figure, ZABC is a parallelogram. BE, EF and ZA are straight lines. ZCD is an isosceles triangle.
- Find ∠a.
- Find ∠b.
(a)
∠BEZ = ∠AZF = 62° (Corresponding angles, ZA//EB)
∠EDZ
= 180° - ∠BEZ - ∠EZD
= 180° - 62° - 21°
= 97° (Angles sum of triangle)
∠CDZ
= 180° - 97°
= 83° (Angles on a straight line)
∠DCZ = ∠CDZ = 83° (Isosceles triangle)
∠a
= ∠DCZ
= 83° (Corresponding angles, AB//ZC)
(b)
∠b
= 180° - 83° - 83°
= 14° (Isosceles triangle ZCD)
Answer(s): (a) 83°; (b) 14°