If a polygon has n sides, the angle at the middle is divided into n equal parts: 360/n. The polygon consists of n isosceles triangles with vertex angle at the centre=360/n. So the size of the equal angles is (180-360/n)/2=90-180n. The interior angles of the polygon are formed by doubling this angle so we're back to 180-360/n. There are n interior angles so the sum of the interior angles is 180n-360. This is equal to 44 right angles or 22*180. So 180n-360=22*180, dividing through by 180: n-2=22 making n=24.