Question

What is the number of sides of a regular polygon in which each interior angle measure 135°?​

Answer 1

Answer:

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

$\frac{(n-2)x180}{n}$

$\frac{(n-2)x180}{n} = 135$

$(n − 2) × 180 = 135n$

$→180n - 360 = 135n$

$180n - 135n = 360$

$→45n = 360$

$→n = \frac{360}{45} = 8$

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