if a regular octagon has a perimeter of 264 centimeters, what is the measure of each interior angle and each side?

To find the measure of each interior angle and each side of a regular octagon, we can use the properties of regular polygons.

A regular octagon has eight sides of equal length and eight equal interior angles. Let's denote the measure of each side as "s" and the measure of each interior angle as "x".

The formula to find the perimeter of any polygon is given by:

Perimeter = Number of Sides * Length of Each Side

In this case, the perimeter of the octagon is given as 264 centimeters:

264 = 8s

Dividing both sides of the equation by 8, we get:

s = 264 / 8
s = 33 centimeters

So, each side of the octagon measures 33 centimeters.

Now, to find the measure of each interior angle, we can use the formula:

Sum of Interior Angles = (Number of Sides - 2) * 180 degrees

In this case, the sum of the interior angles of an octagon is:

Sum of Interior Angles = (8 - 2) * 180 degrees
Sum of Interior Angles = 6 * 180 degrees
Sum of Interior Angles = 1080 degrees

Since all the interior angles of a regular octagon are equal, we can divide the sum by the number of angles:

x = Sum of Interior Angles / Number of Angles
x = 1080 degrees / 8
x = 135 degrees

Therefore, each interior angle of the regular octagon measures 135 degrees.