How do you find the measure of each interior angle in a regular shape using two different methods?
The sum of all the interior angles in a regular shape is given by the formula
180(n-2), where n is the number of sides. To get the size of each individual interior angle, you divide the answer you get from using 180(n-2) by the number of sides.
The sum of the exterior angles in any polygon is 360. To find the size of each exterior angle divide 360 by n (n is the number of sides in the regular shape). Now that gives you the size of the exterior angle. To get the interior angle, all you need to do is 180 - the size of the exterior angle. This is because the interior angle and exterior angle make a straight line, and angles on a straight line add up to 180.