How many sides does a polygon have if each of its interior angles measures 156°?

To find the number of sides of a polygon with interior angles measuring 156°, we can use the formula for the sum of interior angles of a polygon.

The formula is given by: Sum of interior angles = (n - 2) * 180°

Where n represents the number of sides of the polygon.

In this case, we have the information that each interior angle measures 156°.

So, we can set up the equation as follows: 156° * n = (n - 2) * 180°

Simplifying the equation, we get: 156° * n = 180°n - 360°

Rearranging the equation, we have: 180°n - 156°n = 360°

Combining like terms, we get: 24°n = 360°

Dividing both sides of the equation by 24°, we find: n = 15

Therefore, a polygon with each of its interior angles measuring 156° has 15 sides.