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?
Since the shape in question is a regular polygon, we know that all of the interior angles must be the same:
Thus, the size of one of this shape's exterior angles will be:
The sum of the exterior angles of a regular polygon always total to
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:
Our calculation would suggest that our shape is a regular hexagon, which does indeed have interior angles of
We can now find the total of all of our interior angles: we can use this equation to do so:
To verify, dividing our answer by
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.