In a regular polygon, the ratio of the measure of the exterior angle to the measure of the adjacent interior angle is 1:4. How many sides does the polygon have?

Question

please give exact answer

Answer 1

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.