In the figure, TUVW is a parallelogram. O is the centre of the circle. Find
- ∠TWV
- ∠TUW
(a)
∠OUW = ∠UWO = 36° (Angle properties within a circle)
∠WOU
= 180° - 36° - 36°
= 108° (Angles sum of triangle)
∠OTU + ∠OUT = ∠UOW (Exterior angle of a triangle)
∠OTU = ∠OUT (Isosceles triangle, OT = OU)
∠OTU
= 108° ÷ 2
= 54° (Exterior angle of a triangle)
∠TWV
= 180° - 54°
= 126° (Interior angles)
(b)
∠TUW
= 180° - 54° - 36°
= 90° (Angle sum of triangles)
Answer(s): (a) 126°; (b) 90°