A hexagon has exterior angle measures of 59, 70, 68, 58, and 53. What is the measure of the sixth interior angle?

The sum of the exterior angles of any polygon = 360°

Add the other angles together and subtract from 360.

To find the measure of the sixth interior angle of a hexagon, we can use the fact that the sum of all the interior angles of a hexagon is equal to (6 - 2) * 180 degrees.

The formula for finding the sum of the interior angles of a polygon is (n - 2) * 180 degrees, where n is the number of sides of the polygon. In this case, n = 6, so the sum of the interior angles is (6 - 2) * 180 = 4 * 180 = 720 degrees.

Now, we know the measures of five of the exterior angles, which are 59, 70, 68, 58, and 53 degrees. The sum of the measures of the exterior angles of any polygon is always 360 degrees. So, let's find the sum of these five angles: 59 + 70 + 68 + 58 + 53 = 308 degrees.

To find the measure of the sixth interior angle, we subtract the sum of the exterior angles from the sum of the interior angles: 720 - 308 = 412 degrees.

Therefore, the measure of the sixth interior angle of the hexagon is 412 degrees.