Final answer:
To find the greatest exterior angle of a triangle with two interior angles measuring 50 degrees and 45 degrees, we calculate the missing third interior angle and then find the supplementary exterior angle, which is 95 degrees.
Step-by-step explanation:
The question is asking for the greatest measure of the exterior angles of a triangle, given two of its interior angles. We know that the sum of the interior angles of any triangle is 180 degrees. Thus, if two of the interior angles are 50 degrees and 45 degrees, we first find the third interior angle by subtracting the sum of the given angles from 180:
180 degrees - (50 degrees + 45 degrees) = 85 degrees.
The exterior angle is supplementary to the interior angle, meaning they add up to 180 degrees. Therefore, the greatest exterior angle is:
180 degrees - 85 degrees = 95 degrees.
So, the greatest measure of the triangle's exterior angles is 95 degrees.