The radius

The radius 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 diameter.

An isosceles triangle within a circle, the legs equal to the radius of the circle

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.

An isosceles triangle within a circle and a 136∞ angle between the diameter and the radius

\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