The exterior angles of a triangle are in the ratio of 4:5:6. What is the least interior angle

Least interior angle = 36 degrees

Step-by-step explanation:

The ratio 4:5:6 means that the greatest exterior angle is 6 / (4+5+6) = 6/15 of the total value of the angles.

The sum of the exterior angles = 360 degrees so the greatest one is

= 360 * 6 / 15

= 360 * 2/5

= 144 degrees

This is adjacent to the smallest interior angle of the triangle so the answer is 180 - 144 = 36 degrees