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Polygon Interior Angles Sum Theorem

Polygon Interior Angles Sum Theorem

The sum of the measures of the interior angles of a convex polygon with n sides is

( n 2 ) 180 ° .

Example :

Find the sum of the measures of the interior angles of an octagon.

Solution:

An octagon has 8 sides. So, n = 8 .

Substitute 8 for n in the formula.

The sum of the measures of the interior angles of an octagon = ( 8 2 ) 180 ° .

= 6 × 180 ° = 1080 °

The sum of the measures of the interior angles of an octagon is 1080 ° .