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# Find number of sides.

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In a certain regular polygon, the measure of each interior angle is 12 times the measure of each exterior angle. Find the number of sides in this regular polygon.

May 11, 2020

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The formula for the value of each interior angle of a regular polygon is  (n - 2)(180o) / n

Each interior angle = 180o - the exterior angle  and  each exterior anlge = 180o - the interior angle.

"each interor angle is 12 times the measuure of each interior angle"

--->     (n - 2)(180o) / n  =  12 · ( 180o -  (n - 2)(180o) / n )

--->     (n - 2)(180o) / n  =   2160o -  12 · (n - 2)(180o) / n )               [distribute the 12]

--->     (n - 2)(180o) / n  +  12 · (n - 2)(180o) / n )  =  2160o              [add 12 · (n - 2)(180o) / n ) to both side]

--->                                    13 · (n - 2)(180o) / n )  =  2160o              [simplify]

--->                                            13 · (n - 2)(180o)  =  2160o · n        [multiply both sides by n]

--->                                             2340 · n - 4680o  =  2160o · n        [multiply out the left side]

--->                                                          180o · n  =  4680o

--->                                                                     n  =  26 sides

May 12, 2020