The of a circle is a line, which starts at the centre of the circle and ends on a point on the circumference. The radius is half the size of the .

Looking at the diagram above, since OA and OB are radii of the circle, then OA = OB, therefore$$AOB$$ forms an isosceles triangle inside the circle.

Also, note that since $$\Delta AOB$$ is isosceles, then $$\angle OAB = \angle OBA$$, this means that the angles at A and B are equal.

Question

In this circle, calculate the size of $$\angle OBA$$.

$$\angle AOC$$ is a straight angle, so will add up to $$180^\circ$$. This is the straight line $$AC$$.

$$\angle AOB = 180^\circ - 136^\circ = 44^\circ$$. This is the other angle at $$O$$.

$$\Delta AOB$$ is isosceles, so $$\angle OAB = \angle OBA$$ and angles in a triangle will add up to $$180^\circ$$.

This means the angles at $$A$$ and $$B$$ will have $$180^\circ- 44^\circ$$ split between them equally.

$\angle OBA = (180^\circ - 44^\circ ) \div 2 = 68^\circ$