Answer:
(n-2) x 180 degrees where n is the number of sides
Step-by-step explanation:
From one vertex of the polygon you draw triangles inside the polygon. Multiply the number of triangles by 180 since all triangles interior angles add up to 180 degrees.
example
Pentagon has 5 sides. (5-2) x 180 = 540 degrees
This is the same as 180n-360
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Explanation:
Draw any polygon you want. Let's say we draw a hexagon. Split the hexagon into 6 triangles. Check out the diagram below.
The goal is to find what the red angles sum to. Recall that any triangle always has its three angles add to 180 degrees. We have 6 triangles, so all of the angles (red+blue) add to 6*180 = 1080 degrees. However, we don't want to include the blue inner angles. So we'll subtract off 360 since the blue angles add up to this amount (they form a full rotation).
So we have 6*180 - 360 as the expression that represents the sum of the interior angles for this hexagon. The hexagon doesn't have to be a regular polygon.
We can generalize to any polygon and not just hexagons. Simply replace that "6" with n and we get n*180 - 360 which is the same as 180n-360 = 180(n-2)
