Question

Find the value of x in the following figure, where O is the centre of the circle: 

Answer 1

In triangle AOB, OA = OB (radii of the circle), so it is isosceles.

Given ∠OAB = 20°, we also have

∠OBA = 20°.

Sum of angles in triangle AOB:

∠AOB = 180° − 20° − 20° = 140°.

The central angle ∠AOB subtends arc AB, so the measure of arc AB is 140°.

The angle at C, ∠ACB x, is an inscribed angle that subtends the same arc AB. An inscribed angle is half the measure of its intercepted arc, so

x = `1/2 xx 140° = 70°`

x = 70°