The figure is not drawn to scale. ∠FEG = 41°, FE = FG and EK//FJ. Given that ∠m is
12 of ∠j and ∠m is 4 times of ∠k, find
- ∠m
- ∠i
(a)
m : j = 1 : 2
j = 2 m
k : m = 1 : 4
j = 2 x 4= 8
j : k : m = 8 : 1 : 4
∠FGE = 41° (Isosceles triangle)
∠EGH
= 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°
∠m
= 4 x 1 u
= 4 x 17°
= 68°
(b)
∠FGE = ∠FEG = 41° (Isosceles triangle)
∠GLJ = ∠GEK = 68° (Corresponding angles, EK//FJ)
∠i
= 68° - 41°
= 27° (Exterior angle of a triangle)
Answer(s): (a) 68°; (b) 27°
