In the figure, G is the centre of the circle, DG is parallel to EF and ∠EGF = 96°. Find the values of
- ∠i
- ∠j
- ∠k
(a)
∠i
= (180° - 96°) ÷ 2
= 42° (Angle properties within a circle)
(b)
∠DGE = ∠i = 42° (Alternate angles)
∠j
= (180° - 42°) ÷ 2
= 69° (Angle properties within a circle)
(c)
∠k
= 360° - 96° - 42°
= 222° (Angles at a point)
Answer(s): (a) 42°; (b) 69°; (c) 222°