To find the measure of an interior angle of any regular polygon, we use the formula:
180 (n-2) / n,
where n is the number of sides in the regular polygon.
Therefore, if there are 15 sides in the regular polygon, your answer would be
180 (15-2) / 15,
or when simplified,
180 * 13 / 15
2340 / 15
156 degrees.
Thus, the measure of an interior angle of a regular polygon with 15 sides is 156 degrees.