In the figure, RSTU is a parallelogram. O is the centre of the circle. Find
- ∠RUT
- ∠RSU
(a)
∠OSU = ∠SUO = 37° (Angle properties within a circle)
∠UOS
= 180° - 37° - 37°
= 106° (Angles sum of triangle)
∠ORS + ∠OSR = ∠SOU (Exterior angle of a triangle)
∠ORS = ∠OSR (Isosceles triangle, OR = OS)
∠ORS
= 106° ÷ 2
= 53° (Exterior angle of a triangle)
∠RUT
= 180° - 53°
= 127° (Interior angles)
(b)
∠RSU
= 180° - 53° - 37°
= 90° (Angle sum of triangles)
Answer(s): (a) 127°; (b) 90°