Question

write an expression for the sum of the angle measures in a regular polygan with n sides. then wirte an expression for the measure of each angle in a regular polygan with n sides.

Answer 1

If it has n sides you make n right turns to get all the way around the outside and end up going the same direction you were going at the start.
So each right turn is 360/n
Each interior angle is the supplement of that right turn
180 - (360/n)
so each interior angle = (180 n -360)/n

each = 180 (n-2)/n

the sum is then 180(n-2)

check that
triangle 180 (3-2)= 180 sure enough 180
square 180(4-2) = 360 yes