Final answer:
After setting x as the measure of the angle's complement, the algebraic equation x + (x + 86) = 90 is used to find that the complement is 2 degrees and the other angle is 88 degrees, which indicates that none of the provided options are correct.
Step-by-step explanation:
To solve the problem, we need to find the measures of two angles, where one angle's measure is given as 86 degrees greater than its complement. By definition, the complement of an angle is what adds to that angle to make a total of 90 degrees. So, if we let x represent the degree measure of the angle's complement, the other angle will be x + 86 degrees.
Using the fact that the sum of an angle and its complement is 90 degrees, we can set up the following equation:
x + (x + 86) = 90
Solving for x, we find:
- 2x + 86 = 90
- 2x = 90 - 86
- 2x = 4
- x = 2
Hence, the complement is 2 degrees, and the measure of the other angle is x + 86 degrees, which is 2 + 86 = 88 degrees.
None of the given options (a, b, c, d) match our calculated answers. Therefore, the provided options are incorrect based on our calculations.