Final answer:
The measure of the exterior angle is 115 degrees, which is found by subtracting the sum of the opposite interior angles (42 degrees + 23 degrees = 65 degrees) from 180 degrees.
Step-by-step explanation:
If the interior angles opposite the exterior angle measure 42 and 23 degrees respectively, we can find the measure of the exterior angle by using the fact that the sum of the measures of the interior angle and its adjacent exterior angle is 180 degrees. This is because they form a linear pair.
First, we add the two given interior angles: 42 degrees + 23 degrees = 65 degrees. Then, we find the exterior angle by subtracting this sum from 180 degrees: 180 degrees - 65 degrees = 115 degrees. Therefore, the measure of the exterior angle is 115 degrees.