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# A stop sign has the shape of a regular octagon. What is the sum of the interior angles of a stop sign?

Dec 24, 2015

Use the interior sum formula ..

#### Explanation:

Sum $= \left(n - 2\right) \times 180 = \left(8 - 2\right) \times 180 = {1080}^{o}$

hope that helped

Apr 30, 2016

The sum of the interior angles can be calculated easily by understanding where the formula comes from.

For an octagon: Sum = 180 xx 6 = 1080°

#### Explanation:

In any polygon, you can divide it up into triangles by joining one vertex to all of the others. You will find that the number of triangles is ALWAYS 2 less than the number of sides.
ie 3 sides gives 1 triangle. 6 sides gives 4 triangles, 10 sides gives 8 triangles and so on..
But, the sum of the angles in any triangle is always 180°.

So, subtract 2 from the number of sides and multiply by 180°.

This is exactly what $180 \left(n - 2\right)$ tells us, but it is really nice to understand why that formula works. You will never have to learn the formula if you understand it.

An octagon has 8 sides, which means $6$ triangles.

So the sum of the interior angles is:

180 xx 6 = 1080°