Answer:
B. Octagon.
Step-by-step explanation:
We have been given that an interior angle of a regular polygon has a measure of 135°. We are asked to find the type of polygon.
We know that measure of each interior angle of n sides polygon is: [tex]\frac{180(n-2)}{n}[/tex].
We can set an equation as:
[tex]\frac{180(n-2)}{n}=135[/tex]
[tex]\frac{180(n-2)}{n}*n=135*n[/tex]
[tex]180(n-2)=135n[/tex]
[tex]180n-360=135n[/tex]
[tex]180n-135n-360=135n-135n[/tex]
[tex]45n-360=0[/tex]
[tex]45n-360+360=0+360[/tex]
[tex]45n=360[/tex]
[tex]\frac{45n}{45}=\frac{360}{45}[/tex]
[tex]n=8[/tex]
Since number of sides of the given polygon is 8, therefore, the polygon is an octagon and option B is the correct choice.
