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

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

    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(n-2)## 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.

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