Final answer:
The measure of the exterior angle of a triangle, when two interior angles are given as 64 degrees and 75 degrees, is found to be 139 degrees by subtracting the sum of the interior angles from 180 degrees to get the third angle, and then subtracting that from 180 degrees.
Step-by-step explanation:
To find the measure of the exterior angle of a triangle, we first need to find the measure of the third interior angle. Since the sum of the interior angles of a triangle is 180 degrees, we can subtract the given interior angles from 180 degrees:
180 - (64 + 75) = 180 - 139 = 41 degrees.
This 41 degrees is the measure of the third interior angle. The exterior angle is adjacent to the interior angle, and together they form a straight line, which measures 180 degrees. Therefore, we find the measure of the exterior angle by subtracting the interior angle from 180 degrees:
180 - 41 = 139 degrees.
Hence, the correct answer is (a) 139 degrees or (b) 139 degrees.