in a polygon, the sum of the interior angles and the sum of the external angles are equal .how many sides does it have?

The sum of the measures of the exterior angles of a shape is always 360 degrees. 

So we are looking for a shape that has 360 degrees as the sum of the interior angles. 

A quadrilateral has 4 sides. The sum of all the interior angles of a quadrilateral is 360 degree.

So, the polygon has 4 sides (Ans)