The way to understand this is that any polygon with sides greater than or equal to 3 will produce a set of triangles. From basic geometric properties, the angle sum of each triangle is 180°.
Consider a five-sided shape (a pentagon).
From one vertex, we can construct three triangles from the four points we have remaining. This is because the adjacent two points can never construct a triangle.
By doing this, we can see that there are three triangles that we have made. Thus, we know the total summation of angles will have to add up to 180 · 3 = 540°
Now, let's consider a general polygon, one with n sides.
By picking one vertex, we can construct a maximum of (n - 2) triangles, because the two adjacent points do not and will never construct any triangles.
Thus, we can say the sum of the interior angles is generalised as the formula:
180(n - 2)
