Final answer:
The measure of the exterior angle of a triangle with interior angles (x + 8) degrees and 4x degrees is found to be '5x + 8' degrees, which corresponds to option c) x + 8 + 4x.
Step-by-step explanation:
To find the measure of the exterior angle of the triangle with interior angles (x + 8) degrees and 4x degrees, first remember that the sum of the interior angles of any triangle is 180 degrees. With two interior angles known, the third interior angle can be found by using the formula:
180 - (first angle + second angle) = third angle.
For this triangle, the third interior angle is:
180 - ((x + 8) + 4x) = 180 - (5x + 8).
Now, the exterior angle is supplementary to the interior angle at the same vertex, meaning they sum up to 180 degrees. Therefore, the measure of the exterior angle is:
180 degrees - (third interior angle) = 180 degrees - (180 - (5x + 8)) = 5x + 8.
Thus, option c) x + 8 + 4x is the correct expression for the measure of the exterior angle.