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