Interior and External Angles of a Regular Polygon In a Given Ratio
\[n\]sided regular polygon with the interior and exterior angles in the ratio
The interior and exterior angles add up to 180 degrees, so we have to divide 180 in the ratio
The interior angle is
\[11 \times 15 = 165\]degrees and the exterior angle is
\[1 \times 15-15\]degrees.
As the perimeter of the polygon is traced out, an angle of 15 degrees is turned through at each vertex.
\[n\]of these turns are made, adding up to a complete turn of 360 degrees. Hence
The polygon has 24 sides.