I think everyone is using the same formula but doing certain steps in their head and now writing the steps down on paper and that is what is confusing. Start with the basic formula.

If we want to find the value of an interior angle of any polygon the formula is:

\(\frac{180(n-2)}{n}\)

When n = 5 for a pentagon, you get

\(\frac{180(5-2)}{5} = 108\)

So in the picture below, A & B each = 108. If you think of A + B + C as being inside a complete circle (imaginary circle) you know the total must = 360. So 360 - 108 - 108 = 144.

So Angle C in the picture is 144 degrees. This is an interior angle of a polygon formed by all the pentagons being joined. We now have to answer the question: A polygon with how many sides has interior angles of 144? Now we know the answer, but we don't have n. Before we had n =5 (pentagon) but we didn't have the answer. This is basic alegbra.

\(\frac{180(N-2)}{n}=144\)

180(N-2) = 144N

180N - 360 = 144N

36N - 360 = 0

36N = 360

N = 10

So we have created a 10-sided polygon by joining all of those pentagons together.

Attachment:

InteriorAngle.gif [ 4.99 KiB | Viewed 1975 times ]
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J Allen Morris

**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

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