In the figure, G is the centre of the circle, DG is parallel to EF and ∠EGF = 112°. Find the values of
- ∠a
- ∠b
- ∠c
(a)
∠a
= (180° - 112°) ÷ 2
= 34° (Angle properties within a circle)
(b)
∠DGE = ∠a = 34° (Alternate angles)
∠b
= (180° - 34°) ÷ 2
= 73° (Angle properties within a circle)
(c)
∠c
= 360° - 112° - 34°
= 214° (Angles at a point)
Answer(s): (a) 34°; (b) 73°; (c) 214°