The figure, not drawn to scale, O is the centre of the circle and YD // ZC // AB. Find
- ∠XOA
- ∠XCO
(a)
∠DOZ
= 180° - 102°
= 78° (Interior angles, YD//ZO)
∠OAC = ∠OCA = 31° (Isosceles triangle)
∠ZOA
= 31° + 31°
= 62° (Exterior angle of a triangle)
∠XOA
= 78° + 62°
= 140°
(b)
∠COA
= 180° - 31° -31°
= 118° (Isosceles triangle)
∠XOC
= 360° - 140° - 118°
= 102° (Angles at a point)
XO = OC = Radius
∠XCO
= (180° - 102°) ÷ 2
= 78° ÷ 2
= 39° (Isosceles triangle)
Answer(s): (a) 140°; (b) 39°
