The figure, not drawn to scale, O is the centre of the circle and QV // RU // ST. Find
- ∠POS
- ∠PUO
(a)
∠VOR
= 180° - 102°
= 78° (Interior angles, QV//RO)
∠OSU = ∠OUS = 30° (Isosceles triangle)
∠ROS
= 30° + 30°
= 60° (Exterior angle of a triangle)
∠POS
= 78° + 60°
= 138°
(b)
∠UOS
= 180° - 30° -30°
= 120° (Isosceles triangle)
∠POU
= 360° - 138° - 120°
= 102° (Angles at a point)
PO = OU = Radius
∠PUO
= (180° - 102°) ÷ 2
= 78° ÷ 2
= 39° (Isosceles triangle)
Answer(s): (a) 138°; (b) 39°