Question

How do you find the measure of each interior angle of a polygon?

Answer 1

Without more information, you can only find the value of the interior angles of a regular polygon. Using the equation is `((n-2)180^@)/n` where `n` is the number of sides of the regular polygon

Explanation:

A regular polygon refers to a multi-sided convex figure where all sides are equal in length and all angles have equal degree measures.

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![http://proofsfromthebook.com/2012/11/28/sum-of-exterior-angles/]()

The regular triangle has 3 interior angles of `60^@` and 3 exterior angles of `120^@`. The exterior angle have a sum of `360^@ =(3)120^@`

The square has 4 interior angles of `90^o` and 4 exterior angles of `90^@`. The exterior angles have a sum of `360^@ =(4)90^@`.

The pentagon has 5 interior angles of `108^o` and 5 exterior angles of `72^@`. The exterior angles have a sum of `360^@ =(5)72^@`.

In order to find the value of the interior angle of a regular polygon, the equation is `((n-2)180^@)/n` where n is the number of sides of the regular polygon.

Triangle: `" "((3-2)180^@)/3 = 60^@`

Square `" "((4-2)180^@)/4 = 90^@`

Pentagon `" "((5-2)180^@)/5 = 108^@`