The octagon is made up of 8 congruent isosceles triangles
whose legs are radii of the circle.

We know that each of those congruent isosceles triangles 
has a 45°-vertex angle because 360° divided by 8 is 45°.

Because the triangles are isosceles, the base angles
are congruent (equal in measure).  So the sum is found by
subtracting 180°-45° =  135°, and each base angle is half
of that or 67.5°.

Have you studied the law of sines?  There's another way to
get the solution without using the law of sines, but if 
you've studied the law of sines, that's the easiest way:









Or R = 10 cm. to the nearest centimeter.

Edwin