Final answer:
The measure of the third exterior angle of a triangle, given two other angles measuring 103 degrees and 126 degrees, is calculated by subtracting the sum of these two angles from 360 degrees, resulting in 131 degrees for the third angle.
Step-by-step explanation:
To determine the measure of the third exterior angle of a triangle when given the measures of the other two, one must understand that the sum of the exterior angles of a triangle is always 360 degrees. This is because each exterior angle is supplementary to its corresponding interior angle, and the sum of the interior angles of a triangle is 180 degrees. Since the exterior angles are supplementary to the interior angles, each pair adds up to 180 degrees, and there are three pairs for the three sides of the triangle, totaling 360 degrees.
Given that one exterior angle measures 103 degrees and another measures 126 degrees, we can find the measure of the third exterior angle by subtracting the sum of the provided angles from 360 degrees:
360 degrees - (103 degrees + 126 degrees) = 360 degrees - 229 degrees = 131 degrees
Therefore, the measure of the third exterior angle of the triangle is 131 degrees.