How many sides does this polygon have

The sum of the measures of the interior angles of a certain polygon is the same as the sum of the measures of is exterior angles.

The sum of the exterior angles of any closed polygon is 360°
The sum of the interior angles of any closed polygon is 180*(n-2)

360 = 180*(n-2)
2 = n-2
n = 4

The polygon has 4 sides.

Measure of interior angles - 180(n-2) = 180n - 360, where n represents the number of sides.
For any convex polygon, the sum of its exterior angles will be 360°.
So since these values are equal,
180n - 360 = 360
180n = 720
n = 4
The polygon has four sides.