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 = 29° (Isosceles triangle)
∠UOV
= 29° + 29°
= 58° (Exterior angle of a triangle)
∠SOV
= 78° + 58°
= 136°
(b)
∠XOV
= 180° - 29° -29°
= 122° (Isosceles triangle)
∠SOX
= 360° - 136° - 122°
= 102° (Angles at a point)
SO = OX = Radius
∠SXO
= (180° - 102°) ÷ 2
= 78° ÷ 2
= 39° (Isosceles triangle)
Answer(s): (a) 136°; (b) 39°