Each interior angle of a regular polygon measures 140 degrees how many sides does the polygon have

The sum of the measures of the interior angles of a polygon of n sides is
180(n - 2)

If the polygon is regular, all angles are congruent, and each angle measures
[180(n - 2)]/n

Set the measure of one angle equal to 140, and solve for n, the number of sides.

[180(n - 2)]/n = 140

180(n - 2) = 140n

180n - 360 = 140n

40n = 360

n = 9

The number of sides is 9.