Question

An interior angle of a regular polygon has a measure of 135°. What type of polygon is it? hexagon octagon nonagon decagon

Answer 1

Answer: Octagon

Explanation:

$\cfrac{(n-2)\times 180}{n} = 135$

$180n - 360 = 135n$

$45n = 360$

$n = 8$

8-gon = octagon


The Wise Orange remembers that Octopus has 8 feet, so Octagon has 8 sides.

Answer 2

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: $\frac{180(n-2)}{n}$.

We can set an equation as:

$\frac{180(n-2)}{n}=135$

$\frac{180(n-2)}{n}*n=135*n$

$180(n-2)=135n$

$180n-360=135n$

$180n-135n-360=135n-135n$

$45n-360=0$

$45n-360+360=0+360$

$45n=360$

$\frac{45n}{45}=\frac{360}{45}$

$n=8$

Since number of sides of the given polygon is 8, therefore, the polygon is an octagon and option B is the correct choice.