The figure, not drawn to scale, O is the centre of the circle and NT // PS // QR. Find
- ∠MOQ
- ∠MSO
(a)
∠TOP
= 180° - 98°
= 82° (Interior angles, NT//PO)
∠OQS = ∠OSQ = 33° (Isosceles triangle)
∠POQ
= 33° + 33°
= 66° (Exterior angle of a triangle)
∠MOQ
= 82° + 66°
= 148°
(b)
∠SOQ
= 180° - 33° -33°
= 114° (Isosceles triangle)
∠MOS
= 360° - 148° - 114°
= 98° (Angles at a point)
MO = OS = Radius
∠MSO
= (180° - 98°) ÷ 2
= 82° ÷ 2
= 41° (Isosceles triangle)
Answer(s): (a) 148°; (b) 41°