The figure, not drawn to scale, O is the centre of the circle and QV // RU // ST. Find
- ∠POS
- ∠PUO
(a)
∠VOR
= 180° - 96°
= 84° (Interior angles, QV//RO)
∠OSU = ∠OUS = 32° (Isosceles triangle)
∠ROS
= 32° + 32°
= 64° (Exterior angle of a triangle)
∠POS
= 84° + 64°
= 148°
(b)
∠UOS
= 180° - 32° -32°
= 116° (Isosceles triangle)
∠POU
= 360° - 148° - 116°
= 96° (Angles at a point)
PO = OU = Radius
∠PUO
= (180° - 96°) ÷ 2
= 84° ÷ 2
= 42° (Isosceles triangle)
Answer(s): (a) 148°; (b) 42°