The figure is not drawn to scale. ∠ZYA = 41°, ZY = ZA and YD//ZC. Given that ∠v is
12 of ∠s and ∠v is 4 times of ∠t, find
- ∠v
- ∠r
(a)
v : s = 1 : 2
s = 2 v
t : v = 1 : 4
s = 2 x 4= 8
s : t : v = 8 : 1 : 4
∠ZAY = 41° (Isosceles triangle)
∠YAB
= 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°
∠v
= 4 x 1 u
= 4 x 17°
= 68°
(b)
∠ZAY = ∠ZYA = 41° (Isosceles triangle)
∠AEC = ∠AYD = 68° (Corresponding angles, YD//ZC)
∠r
= 68° - 41°
= 27° (Exterior angle of a triangle)
Answer(s): (a) 68°; (b) 27°
