Question

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

Answer 1

So basically the regular polygon interior angles don't really have an efficient strategy to figure out, there is a formula but it would be better just to memorize it.
Kind of chart below:

Shape              Number of Sides     Total Interior Angle    Single Interior Angle

Triangle            3 sides                     180 degrees             60 degrees
Quadrilateral    4 sides                     360 degrees             90 degrees
Pentagon         5 sides                      540 degrees            108 degrees
Hexagon          6 sides                      720 degrees            120 degrees
Heptagon         7 sides                      900 degrees            129 ish degrees
Octagon           8 sides                      1080 degrees          135 degrees

So it is an octagon.

Answer 2

ANSWER

$\boxed {Octagon}$

EXPLANATION


The interior angle of a regular polygon with n sides can be found using the formula,

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

It was given that, the interior angle is 135°.



This implies that,


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


We cross multiply to obtain,


$(n - 2)180 = 135n$


We expand to obtain;


$180 n - 360 = 135n$


Group like terms to get,

$180n - 135n = 360$


$45n = 360$


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

$n = 8$