Question

a regular polygon with each interior angle as 108 degree is a​

Answer 1

Pentagon

please mark it as brainliest

Answer 2

Hey there!

There is a formula to determine the sum of all the interior angles of a polygon, which is:

$sum = \left(n - 2\right) \times 180$°, where $n$ is the number of sides it has.

We know that each angle is equal in a regular polygon. So if we divide the $sum$ of the angles (as shown above) with the $n$umber of sides, then it will be equal to the measure of one angle, which is given as 108°.

$\dfrac{sum}{n} = 108$

But we also know the formula for the $sum$, as shown in the beginning! So let's substitute it here:

$\dfrac{sum}{n} = 108$

$\dfrac{\left(n - 2\right) \times 180}{n} = 108$

$\dfrac{180n - 360}{n} = 108$

Taking $n$ to the right hand side, we get:

$180n -360 = 108n$

$-360 = 108n - 180n$

$-360 = -72n$

$n = \dfrac{-360}{-72}$

$n = 5$

Therefore, a regular polygon with 5 sides, which is also known as a Pentagon, has each interior angle as 108°.

Important points/concepts to remember:

1. Formula of sum of all angles of a polygon
2. Each angle in a regular polygon is equal