The figure is not drawn to scale. ∠YXZ = 41°, YX = YZ and XC//YB. Given that ∠g is
12 of ∠e and ∠g is 4 times of ∠f, find
- ∠g
- ∠d
(a)
g : e = 1 : 2
e = 2 g
f : g = 1 : 4
e = 2 x 4= 8
e : f : g = 8 : 1 : 4
∠YZX = 41° (Isosceles triangle)
∠XZA
= 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°
∠g
= 4 x 1 u
= 4 x 17°
= 68°
(b)
∠YZX = ∠YXZ = 41° (Isosceles triangle)
∠ZDB = ∠ZXC = 68° (Corresponding angles, XC//YB)
∠d
= 68° - 41°
= 27° (Exterior angle of a triangle)
Answer(s): (a) 68°; (b) 27°
