The figure, not drawn to scale, O is the centre of the circle and TY // UX // VW. Find
- ∠SOV
- ∠SXO
(a)
∠YOU
= 180° - 102°
= 78° (Interior angles, TY//UO)
∠OVX = ∠OXV = 34° (Isosceles triangle)
∠UOV
= 34° + 34°
= 68° (Exterior angle of a triangle)
∠SOV
= 78° + 68°
= 146°
(b)
∠XOV
= 180° - 34° -34°
= 112° (Isosceles triangle)
∠SOX
= 360° - 146° - 112°
= 102° (Angles at a point)
SO = OX = Radius
∠SXO
= (180° - 102°) ÷ 2
= 78° ÷ 2
= 39° (Isosceles triangle)
Answer(s): (a) 146°; (b) 39°