The interior angle of a regular polygon is four times its exterior angle .find the number of sides of the polygon
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Answer: 10 sides
If the interior angle is 4 times the exterior angle, then both angles together must sum to 5 times the exterior angle.
4x+x=5x
The interior angle plus the exterior angle is 180 degrees. If you divide that by 5, you’ll have the exterior angle.
180÷5=36
The sum of the exterior angles is 360. Divide that by the exterior angle and you have the number of angles, hence the number of sides.
360÷36=10
That’s 10 sides.
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