What is the sum of the measures of the interior angles of a 14-gon?

Here, we know, sum of the exterior angles is always 360 degrees. 

As there are 14 angles in 14-gon, each exterior angle will measure 360/14 = 180/7 degrees. 

Now, as exterior & interior angle is always supplementary. It would be:
So, each interior angle will measure 180 - 180/7 = 1080/7 = 154.3

Now, sum of 14 angles would be: 154.3 * 14 = 2160 degree

In short, Your Answer would be 2160 degree

Hope this helps!