The figure, not drawn to scale, O is the centre of the circle and NT // PS // QR. Find
- ∠MOQ
- ∠MSO
(a)
∠TOP
= 180° - 96°
= 84° (Interior angles, NT//PO)
∠OQS = ∠OSQ = 31° (Isosceles triangle)
∠POQ
= 31° + 31°
= 62° (Exterior angle of a triangle)
∠MOQ
= 84° + 62°
= 146°
(b)
∠SOQ
= 180° - 31° -31°
= 118° (Isosceles triangle)
∠MOS
= 360° - 146° - 118°
= 96° (Angles at a point)
MO = OS = Radius
∠MSO
= (180° - 96°) ÷ 2
= 84° ÷ 2
= 42° (Isosceles triangle)
Answer(s): (a) 146°; (b) 42°