Draw a circle with all the points on the circumference and the centre labelled. Also, connect each points to the centre.

There are 6 different isosceles triangles with different base angles, call them angle 1, angle 2, angle 3, angle 4, angle 5, angle 6.

For each triangle, the remaining angle is 180-2(base angle)

Ex: For triangle OBC, remaining angle is 180-2(angle 1)

The sum of all remaining angles is 360.

180-2(angle 1)+180-2(angle 2)+...+180-2(angle 6)=360

Simplify this, angle 1 + angle 2 +...+ angle 6=360

angle ABC = angle 2 + angle 1

angle CDE = angle 6 + angle 5

angle EFA = angle 3 + angle 4

...