To find the sum of the interior angles in a regular polygon use the formula 180(n-2) where n is the number of sides in the polygon. In the case of a decagon this yields the formula 180(10-2) = 1440. An alternate way to do this is to use the formula 180 - (360/n) to calculate the interior angle, which is 144 degrees for a decagon, and then multiply it by the number of angles, 10, to give you 1440.
Take the total number of sides -2 and multiples that number times 180. This will work for any normal polygon with any number of sides. Once you have that number divide by the total number of sides this is the measurement per angle.