In the figure, G is the centre of the circle, DG is parallel to EF and ∠EGF = 108°. Find the values of
- ∠e
- ∠f
- ∠g
(a)
∠e
= (180° - 108°) ÷ 2
= 36° (Angle properties within a circle)
(b)
∠DGE = ∠e = 36° (Alternate angles)
∠f
= (180° - 36°) ÷ 2
= 72° (Angle properties within a circle)
(c)
∠g
= 360° - 108° - 36°
= 216° (Angles at a point)
Answer(s): (a) 36°; (b) 72°; (c) 216°