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OK Math Cadets, we’re going to derive our own formula. First, let’s extend this pattern. How many triangles can you break a pentagon into? What about a Hexagon? Complete the following table and see if you can find a relationship between the number of sides and the number of triangles. Need a hint? Click the “Hint” button below.
Pentagon
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Hexagon
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Heptagon
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Octagon
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Not sure how to create your triangles? Just pick any 1 vertex, and draw a line from it to each of the other vertices. Voila! You just broke your shape into triangles!
Alright, we’re almost ready to create our own formula. As we have seen, every time we add a side, we add 180 degrees to the interior angle sum. Unfortunately, we can’t just multiply 180 by the number of sides. If we did, a triangle’s angles would add to 540 degrees, instead of 180. Let “n” be the number of sides in a polygon. Can you figure our a formula using “n” for the sum of the interior angles?
Remember, we need at least 3 sides to make a polygon, so there can’t be 1 or 2 sided figures. For every side OVER 3, we add 180 degrees.
What if we want to know the measure of one specific angle in a regular polygon? How can we modify our formula to find the measure of an interior angle in a regular polygon? Remember, in a regular polygon each interior angle is equal.