Question

find the number of side of a regular polygon whose each of interior angle is 135 degree​

Answer 1

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Answer 2

Complete step-by-step answer:

We are given that each interior angle is 135∘,

we have to find the number of sides of the polygon. Let’s start with the assumption that the number of sides be n, this means that we have n sided regular polygon whose interior angle is 135∘.

We know that their relation between the interior angle and the number of sides of the polygon is given as,

Sum of all interior angles=(n−2)×180∘

Our n sided regular polygon has n interior angles with each of 135 degrees. So, the sum of all the interior angles will be

Sum of all interior angles=n×135∘

So, as we have the sum of all the interior angles given as (n−2)×180∘,

so, we get,

⇒n×135∘=(n−2)×180∘

Now, opening the brackets, we get,

⇒135n=180n−360∘

Now simplifying the term, we get,

⇒136n−180n=−360

Solving for n, we get,

⇒−45n=−360

Dividing both sides by – 45, we get,

n=−360−45=8

Therefore, we get the number of sides that the polygon has as 8

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