The figure is not drawn to scale. ∠EDF = 41°, ED = EF and DJ//EH. Given that ∠k is
12 of ∠i and ∠k is 4 times of ∠j, find
- ∠k
- ∠h
(a)
k : i = 1 : 2
i = 2 k
j : k = 1 : 4
i = 2 x 4= 8
i : j : k = 8 : 1 : 4
∠EFD = 41° (Isosceles triangle)
∠DFG
= 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°
∠k
= 4 x 1 u
= 4 x 17°
= 68°
(b)
∠EFD = ∠EDF = 41° (Isosceles triangle)
∠FKH = ∠FDJ = 68° (Corresponding angles, DJ//EH)
∠h
= 68° - 41°
= 27° (Exterior angle of a triangle)
Answer(s): (a) 68°; (b) 27°