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 = 28° (Isosceles triangle)
∠POQ
= 28° + 28°
= 56° (Exterior angle of a triangle)
∠MOQ
= 84° + 56°
= 140°
(b)
∠SOQ
= 180° - 28° -28°
= 124° (Isosceles triangle)
∠MOS
= 360° - 140° - 124°
= 96° (Angles at a point)
MO = OS = Radius
∠MSO
= (180° - 96°) ÷ 2
= 84° ÷ 2
= 42° (Isosceles triangle)
Answer(s): (a) 140°; (b) 42°