Question

Suppose that in a certain triangle, the degree measures of the exterior angles are in the ratio 2:3:4. If the largest interior angle measures y degrees, what is the value of y?

Answer 1

first you should calculate total of the ratios:
2+3+4=9
then divide 360 by 9 (because the total degrees of the exterior angles in polygon is 360)

`360 / 9 = 40`
at the end find the amount of the exterior angles:

`2 * 40 = 80 \\ 3 * 40 = 120 \\ 4 * 40 = 160`
the shortest exterior angle is 80 degrees
so it has the largest interior angle:
180-80=100
the answer is 100