The figure, not drawn to scale, O is the centre of the circle and PU // QT // RS. Find
- ∠NOR
- ∠NTO
(a)
∠UOQ
= 180° - 96°
= 84° (Interior angles, PU//QO)
∠ORT = ∠OTR = 31° (Isosceles triangle)
∠QOR
= 31° + 31°
= 62° (Exterior angle of a triangle)
∠NOR
= 84° + 62°
= 146°
(b)
∠TOR
= 180° - 31° -31°
= 118° (Isosceles triangle)
∠NOT
= 360° - 146° - 118°
= 96° (Angles at a point)
NO = OT = Radius
∠NTO
= (180° - 96°) ÷ 2
= 84° ÷ 2
= 42° (Isosceles triangle)
Answer(s): (a) 146°; (b) 42°