In the figure, ZABC is a parallelogram. BE, EF and ZA are straight lines. ZCD is an isosceles triangle.
- Find ∠k.
- Find ∠m.
(a)
∠BEZ = ∠AZF = 58° (Corresponding angles, ZA//EB)
∠EDZ
= 180° - ∠BEZ - ∠EZD
= 180° - 58° - 20°
= 102° (Angles sum of triangle)
∠CDZ
= 180° - 102°
= 78° (Angles on a straight line)
∠DCZ = ∠CDZ = 78° (Isosceles triangle)
∠k
= ∠DCZ
= 78° (Corresponding angles, AB//ZC)
(b)
∠m
= 180° - 78° - 78°
= 24° (Isosceles triangle ZCD)
Answer(s): (a) 78°; (b) 24°