For a convex 40-gon, what is the sum of the measures of the interior angles?

The sum of the measures of a polygon's interior angles will always be:

(n - 2) 180° where n is the number of sides/angles.

Plug 40 in for n:

angle sum = (n - 2) 180

sum = (40 - 2) 180

sum = 38 * 180 = 6840

Thus, the sum of the interior measures of a 40-gon is 6840°.