The sum of the interior angles of a polygon will add up to 180 degrees. Four sides give you two triangles and that's the least amount you need to have a polygon. Every additional side after 4 will get you another triangle. So now that you know the basic information lets explain how the formula makes sense. First lets add a 2 to the equation for how many triangles are required count as polygon.
#triangles = 2
Next you need to factor in how each side after 4 sides are an extra triangle and since you already put down 2 triangle which is equal to 4 sides you need to subtract the required amount of sides by additional sides of a polygon.
#triangles = 2 + ( s - 4 )
After that you just simplify that equation to...
#triangles = ( s - 2 )
Finally you need to factor in the the degrees and since every triangle's sum of interior angles add up to 180 degrees that is the number you have to multiply against.
sum of interior angles of a polygon = ( s - 2 ) x 180.
I now it's wordy and repeats a lot, but I think its a good enough explain of how to find the sum of the interior angles of any polygon :)
