Answer: 135°
Step-by-step explanation: In this problem, we're asked to find the measure of each interior angle of a regular octagon.
So let's use our formula for finding the measure of
each interior angle of a regular octagon which is [tex]\frac{180(n - 2)}{n}[/tex].
In this formula, n represents the
number of sides of the polygon.
Remember that an octagon is a polygon that has 8 sides
so we plug a 8 in for n and we have [tex]\frac{180(8 - 2)}{8}[/tex].
Simplifying across the top, (8 - 2) is 6so we have [tex]\frac{180(6)}{8}[/tex].
180(6) is 1,080 so we have [tex]\frac{1,080}{8}[/tex] and
1,080 divided by 8 gives us 135.
So the measure of each interior angle of a regular octagon is 135°.
I have also attached my work below.
