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 = 30° (Isosceles triangle)
∠POQ
= 30° + 30°
= 60° (Exterior angle of a triangle)
∠MOQ
= 84° + 60°
= 144°
(b)
∠SOQ
= 180° - 30° -30°
= 120° (Isosceles triangle)
∠MOS
= 360° - 144° - 120°
= 96° (Angles at a point)
MO = OS = Radius
∠MSO
= (180° - 96°) ÷ 2
= 84° ÷ 2
= 42° (Isosceles triangle)
Answer(s): (a) 144°; (b) 42°