An interior angle of a regular convex polygon is 135 degrees. How many sides does the polygon have?

The formula for the sum of the interior angles of a polygon is (n-2) * 180, where n is the number of sides. Then you would divide the sum by the number of sides to find what one angle is.

Knowing the angle you can calculate n (number of sides):

(n-2) * 180 / n = 135

Use distributive property:

180n - 360 / n = 135

Multiply both sides by n:

180n - 360 = 135n

add 360 to both sides:

180n = 135n + 360

Subtract 135n from both sides:

45n = 360

Divide both sides by 45:

n = 360 / 45

n = 8

The polygon has 8 sides.