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

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The polygon has 8 sides.

Step-by-step explanation:

Use the sum of interior angles formula to solve.

The sum of the interior angles is equal to (n-2)180. If 135° is one angle, we can simply set up an expression to represent this situation:

135 = (n-2)· 180 / n

Multiply both sides by n:

135n = (n-2) · 180

Distribute the 180:

135n = 180n - 360

Subtract 180n from both sides:

-45n = -360

Divide both sides by -45:

n = 8. The polygon has 8 sides.

8 sides

Step-by-step explanation:

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