Exterior angle of a regular polygon is equal to interior angle. Find number of sides in polygon

The exterior angle and the interior angle of a polygon are related by the formula:

Interior Angle + Exterior Angle = 180 degrees

Given that the exterior angle is equal to the interior angle, we can set up the equation:

Interior Angle + Interior Angle = 180 degrees 2 * Interior Angle = 180 degrees Interior Angle = 180 degrees / 2 Interior Angle = 90 degrees

The number of sides n of a regular polygon is given by the formula:

n = 360 degrees / Exterior Angle

Since the exterior angle is equal to the interior angle, and we've found that the interior angle is 90 degrees, we can substitute:

n = 360 degrees / 90 degrees n = 4

So, the polygon is a quadrilateral, or a 4-sided polygon.