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Suppose every interior angle in a regular polygon is approximately 152.31∘. What kind of polygon is this?

Sagot :

To solve this question, we have to understand the sum of all angles of a polygon and identify the polygon, which is classified according to the number of sides, getting that, since the polygon has 13 sides, it is a tridecagon.

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Sum of angles:

The sum of angles of a polygon of n sides is given by:

[tex]S_n = 180(n-2)[/tex]

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Regular polygon, with interior angles of 152.31∘.

In a regular polygon, all of the n angles have the same measure, which means that the sum of the angles is:

[tex]S_n = 152.31n[/tex]

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Finding n:

To classify the polygon, we have to find n, which we do equaling the two equations for [tex]S_n[/tex]. Then

[tex]180(n-2) = 152.31n[/tex]

[tex]180n - 152.31n = 360[/tex]

[tex]27.69n = 360[/tex]

[tex]n = \frac{360}{27.69}[/tex]

[tex]n = 13[/tex]

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Since the polygon has 13 sides, it is a tridecagon.

A similar question is found at https://brainly.com/question/24327450

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