The figure, not drawn to scale, O is the centre of the circle and NT // PS // QR. Find
- ∠MOQ
- ∠MSO
(a)
∠TOP
= 180° - 102°
= 78° (Interior angles, NT//PO)
∠OQS = ∠OSQ = 29° (Isosceles triangle)
∠POQ
= 29° + 29°
= 58° (Exterior angle of a triangle)
∠MOQ
= 78° + 58°
= 136°
(b)
∠SOQ
= 180° - 29° -29°
= 122° (Isosceles triangle)
∠MOS
= 360° - 136° - 122°
= 102° (Angles at a point)
MO = OS = Radius
∠MSO
= (180° - 102°) ÷ 2
= 78° ÷ 2
= 39° (Isosceles triangle)
Answer(s): (a) 136°; (b) 39°