The figure is not drawn to scale. ZA//CB and BA//DZ. Triangles ZDA and ABC are isosceles triangles. Find
- ∠y
- ∠z.
(a)
∠ABC = ∠AZD = 72° (BA//DZ, AZ//BC)
∠ZAD
= (180° - 72°) ÷ 2
= 108° ÷ 2
= 54° (Isosceles triangle)
∠BAC
= 180° - 72° - 72°
= 36° (Isosceles triangle)
∠y
= 180° - 72° - 54° - 36°
= 18° (Interior angles, AZ//BC)
(b)
∠z
= 180° - 27° - 18°
= 135° (Angles sum of triangle)
Answer(s): (a) 18°; (b) 135°