calculate <AOB, <ACB, <ABC

Question

for the figure whose AB is a side of a regular six-sided polygon and AC is a side of a regular eight-sided polygon inscribed in the circle with centre O. join O with A and B

Answer 1

More information is needed to answer this question. Specifically, we need to know where exactly point C is with respect to the hexagon containing AB.

 

Are we to assume that the regular six-sided polygon (or hexagon) is hexagon ABCDEF, so that triangle ABC is composed of the three consecutive points around the perimeter of the hexagon?

 

There are infinite possibilities for the sizes and locations of the polygons and circle O in relation to each other, based only on the information provided.