The figure is not drawn to scale. ∠AZB = 41°, AZ = AB and ZE//AD. Given that ∠z is
12 of ∠x and ∠z is 4 times of ∠y, find
- ∠z
- ∠w
(a)
z : x = 1 : 2
x = 2 z
y : z = 1 : 4
x = 2 x 4= 8
x : y : z = 8 : 1 : 4
∠ABZ = 41° (Isosceles triangle)
∠ZBC
= 180° - 41°
= 139° (Angles on a straight line)
1 u + 4 u + 8 u + 139° = 360° (Sum of angles in a quadrilateral)
13 u = 360° - 139° = 221°
1 u = 221 ÷ 13 = 17°
∠z
= 4 x 1 u
= 4 x 17°
= 68°
(b)
∠ABZ = ∠AZB = 41° (Isosceles triangle)
∠BFD = ∠BZE = 68° (Corresponding angles, ZE//AD)
∠w
= 68° - 41°
= 27° (Exterior angle of a triangle)
Answer(s): (a) 68°; (b) 27°
