In the figure, X is the centre of the circle, UX is parallel to VW and ∠VXW = 108°. Find the values of
- ∠q
- ∠r
- ∠s
(a)
∠q
= (180° - 108°) ÷ 2
= 36° (Angle properties within a circle)
(b)
∠UXV = ∠q = 36° (Alternate angles)
∠r
= (180° - 36°) ÷ 2
= 72° (Angle properties within a circle)
(c)
∠s
= 360° - 108° - 36°
= 216° (Angles at a point)
Answer(s): (a) 36°; (b) 72°; (c) 216°