Find the sum of the measures of the interior angles of a convex 30-gon.

There's an equation for that:

Sum of interior angles = 180 (n - 2)

where n = number of sides

So if you have a polygon with 30 sides, the sum of the interior angles is:

180 (30 - 2) = 180 (28) = 5040 deg

The sum of the interior angles of a polygon with N sides is (N-2) x 180 degrees.

For a 30-gon, the sum of interior angles is (28) x (180) = 5,040 degrees.

It makes no difference whether or not the polygon is convex at every vertex.