The figure is not drawn to scale. It shows a parallelogram GHJK and an isosceles triangle DGK next to it. ∠FKD = 8°. FE and DC are straight lines. Find
- ∠n
- ∠l + ∠m
- ∠m
(a)
∠n
= 180° - ∠FKD
= 180° - 8°
= 172° (Angles on a straight line)
(b)
∠l = ∠GKJ (Parallelogram)
∠l + ∠m
= 180° - 8° - 57°
= 115° (Angles on a straight line)
(c)
∠DGK = ∠l (Corresponding angles)
∠DGK = ∠KDG (Isosceles triangle)
∠l
= 180° - (∠l + ∠m)
= 180° - 115°
= 65°
∠m
= 180° - ∠l - ∠l
= 180° - 65° - 65°
= 50° (Angles sum of triangle)
Answer(s): (a) 172°; (b) 115°; (c) 50°