Final answer:
None of the provided options (a, b, c, d) represent possible measures of interior angles for a triangle with an exterior angle of 150 degrees since the sums do not match the exterior angle, or the angles are not possible for a triangle.
Step-by-step explanation:
The question asks us to find possible measures of interior angles for a triangle with an exterior angle of 150 degrees. By the exterior angle theorem, the sum of the two non-adjacent interior angles must be equal to the exterior angle. Given the options provided:
- Option a (30, 60, 150 degrees): This cannot be correct since the sum of 30 and 60 equals 90, not 150 degrees.
- Option b (90, 45, 15 degrees): The sum of 45 and 15 equals 60, which is not equal to the exterior angle of 150 degrees.
- Option c (120, 30, 75 degrees): Here, 30 and 75 add up to 105, which does not equal the exterior angle of 150 degrees.
- Option d (180, 60, 90 degrees): This cannot be correct as the interior angles of a triangle cannot include an angle of 180 degrees; a triangle's angles must all be less than 180 degrees and sum up to 180 degrees.
None of the provided options represent possible measures of interior angles for a triangle with an exterior angle of 150 degrees.