Question

If an regular interior angle of a regular polygon is 140 degrees, how many sides does the polygon have and I need the work

Answer 1

9 sides

Explanation:

exterior angle + interior angle = 180° , so

exterior angle + 140° = 180° ( subtract 140° from both sides )

exterior angle = 40°

The sum of the exterior angles of a polygon = 360°

Dividing sum by the measure of 1 exterior angles gives number of sides

number of sides =
`(360)/(40)` = 9