The sum of the measures of the internal angles that a convex polygon through n sides is

( n − 2 ) 180 ° .


instance :

find the sum of the steps of the interior angles of an octagon.

Solution:

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

instead of 8 because that n in the formula.

The sum of the steps of the inner angles of one octagon = ( 8 − 2 ) 180 ° .

= 6 × 180 ° = 1080 °

The amount of the measures of the internal angles of an octagon is 1080 ° .


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