2. A regular polygon inscribed in a circle will have all of its central angles the same. We know that a full turn around a circle is 360°. If we break that up into five equal parts for a pentagon then each central angle will be 72°. So, for an octagon we need eight equal central angles of 360° / 8 = 45°. So draw spokes (radii) from the centre of the circle 45° apart, and where they meet the circle will be the vertices of the octagon.