Question

each interior angle of a polygon is 135 how many sides does it have

Answer 1

It is a octagon ( eight sides ).

Because each angle is 135°
so, 1080/ 8 = 135° .

Hence 1080 is divided by 8 , so number of sides = 8

Answer 2

The regular polygon has 8 sides. It is a regular octagon.

Step-by-step explanation:

Given,

Each interior angle of a polygon = 135°

To find, the number of sides of polygon(n) = ?

We know that,

Each interior angle of a regular convex n-gon has a measure of

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

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

⇒ $(n-2)\times 180=135n$

⇒ $180n-360=135n$

⇒$180n-135n=360$

⇒$45n=360$

⇒ $n=\dfrac{360}{45} =8$

Hence, the regular polygon has 8 sides. It is a regular octagon.