m is equal to 90 degrees and n is equal to 115 degrees
We can find m simply by noting that the supplementary angle with it is equal to 90 degrees. This makes m also 90 degrees.
For n, we have to do a bit more work. We know that interior angles of a pentagon add up to 540. So we can add all of the angles together and set equal to that. Since we don't know many of the interior angles, we can find them by looking at their supplements.
113 + 107 + n + n + 90 = 540
310 + 2n = 540
2n = 230
n = 115
11 feet 6 inches and 8 feet 6 inches