The figure is not drawn to scale. ∠AZB = 41°, AZ = AB and ZE//AD. Given that ∠w is
13 of ∠t and ∠w is 4 times of ∠v, find
- ∠w
- ∠s
(a)
w : t = 1 : 3
t = 3 w
v : w = 1 : 4
t = 3 x 4= 12
t : v : w = 12 : 1 : 4
∠ABZ = 41° (Isosceles triangle)
∠ZBC
= 180° - 41°
= 139° (Angles on a straight line)
1 u + 4 u + 12 u + 139° = 360° (Sum of angles in a quadrilateral)
17 u = 360° - 139° = 221°
1 u = 221 ÷ 17 = 13°
∠w
= 4 x 1 u
= 4 x 13°
= 52°
(b)
∠ABZ = ∠AZB = 41° (Isosceles triangle)
∠BFD = ∠BZE = 52° (Corresponding angles, ZE//AD)
∠s
= 52° - 41°
= 11° (Exterior angle of a triangle)
Answer(s): (a) 52°; (b) 11°
