The measure of an interior angle of regular polygon four times the measure of an exterior angle of the same polygon . what is the name of the polygon

Each Exterior Angle = (360 degrees) ÷ (Number of Sides)
Each Interior Angle = 180 - (360 / Number of Sides)

Therefore, since one angle is 4 times the other then,

4 * (360 degrees) / (Number of Sides) = 180 - (360 / Number of Sides)

Number of sides = 10 (it is a decagon)