# You need to construct a regular polygon. When you draw two sides, the interior angle created between them is 120°. What will be the sum, in degrees, of the measures of the interior angles of this polygon when it is completed?

Thus, the size of one of this shape's exterior angles will be:

We can now calculate the number of exterior angles the shape has and, since an exterior angle is formed by the extension of one side of the shape, this will also equate to the number of sides the shape has:

We can now find the total of all of our interior angles: we can use this equation to do so:

Observe that both of our equations to find the total of the shape's interior angles require us to know the number of sides the shape has. This was a piece of information with which we were not provided: this is why we had to work this out using exterior angles.

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The sum of the interior angles of a polygon can be calculated using the formula: Sum = (n - 2) * 180°, where 'n' is the number of sides of the polygon. Since the interior angle of the regular polygon is 120°, the exterior angle is 180° - 120° = 60°. For a regular polygon, the exterior angle is equal to the interior angle. Therefore, each exterior angle is 120°. The number of sides, 'n', can be found by dividing 360° (the total degrees in a circle) by the measure of each exterior angle, which is 120°. Hence, n = 360° / 120° = 3. Substituting 'n' into the formula, Sum = (3 - 2) * 180° = 1 * 180° = 180°. Thus, the sum of the measures of the interior angles of the completed regular polygon is 180°.

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