Exterior angles on Pentagon

Question

the measures of the exterior angles of a pentagon are in a ratio of 1:2:3:4:5. The measure of the largest exterior angle is?.

Answer 1

1, 2, 3, 4, 5 are the parts. The whole is 1+2+3+4+5 = 15. So the largest exterior angle is (largest part)/(whole) = 5/15 = 1/3 of the sum of the exterior angles. In a polygon, the exterior angles always sum to 360°, so the largest exterior angle is (1/3)(360°) = 120°.

Answer 2

I am going to assume that the interior angles of a pentagon has the same ratio as stated in the problem.

I can sub-divide a pentagon into 3 triangles which tells me that the total amount of degrees in a pentagon is 540. I can model the ratio of the interior angles as x + 2x + 3x + 4x + 5x = 540 -------> 15x = 540 ----> x = 36 which is the smallest interior angle. The largest interior angle is 5x = 5(36) = 180. The largest exterior angle would be 360 - 180 = 180 degrees.