In the figure, RSTU is a parallelogram. O is the centre of the circle. Find
- ∠RUT
- ∠RSU
(a)
∠OSU = ∠SUO = 27° (Angle properties within a circle)
∠UOS
= 180° - 27° - 27°
= 126° (Angles sum of triangle)
∠ORS + ∠OSR = ∠SOU (Exterior angle of a triangle)
∠ORS = ∠OSR (Isosceles triangle, OR = OS)
∠ORS
= 126° ÷ 2
= 63° (Exterior angle of a triangle)
∠RUT
= 180° - 63°
= 117° (Interior angles)
(b)
∠RSU
= 180° - 63° - 27°
= 90° (Angle sum of triangles)
Answer(s): (a) 117°; (b) 90°