Final answer:
To find the measure of the angle, we can set up an equation using the definition of a complementary angle.
Step-by-step explanation:
To solve this problem, we need to set up an equation. Let's call the measure of the angle x.
If the measure of an angle is 80 degrees greater than its complement, we can set up the equation to solve for the angle. To do that, let's call the angle x. Its complement will be 90 - x, since complementary angles add up to 90 degrees. The problem states that x is 80 degrees greater than its complement, so:
The complement of the angle is 90 degrees minus the angle, so the measure of the complement is 90 - x. We know that the angle is 80 degrees greater than its complement, so we can write the equation x = 90 - x + 80.
Simplifying the equation, we get 2x = 170. Dividing both sides by 2, we find that x = 85.
Therefore, the measure of the angle is 85 degrees, which is not one of the given answer choices.