The exterior angle is 360/n where n is the number of sides. The adjacent interior angle is 180-360/n.
If this is 4 times the exterior angle then 180-360/n=4*360/n; divide through by 180: 1-2/n=8/n.
So 10/n=1 and n=10. The polygon has 10 sides. The interior angle is 144=4*36.