The figure, not drawn to scale, O is the centre of the circle and QV // RU // ST. Find
- ∠POS
- ∠PUO
(a)
∠VOR
= 180° - 94°
= 86° (Interior angles, QV//RO)
∠OSU = ∠OUS = 31° (Isosceles triangle)
∠ROS
= 31° + 31°
= 62° (Exterior angle of a triangle)
∠POS
= 86° + 62°
= 148°
(b)
∠UOS
= 180° - 31° -31°
= 118° (Isosceles triangle)
∠POU
= 360° - 148° - 118°
= 94° (Angles at a point)
PO = OU = Radius
∠PUO
= (180° - 94°) ÷ 2
= 86° ÷ 2
= 43° (Isosceles triangle)
Answer(s): (a) 148°; (b) 43°