Final answer:
The measures of the two complementary angles in question are calculated to be 47 degrees and 43 degrees, respectively.
Step-by-step explanation:
The question involves finding the measure of two complementary angles with a specific relationship between their sum and difference.
Two angles are complementary if they add up to 90 degrees. The problem states that the sum of the measures of the angles exceeds the difference of their measures by 86 degrees. We can set up an equation to solve this problem:
Let x be the measure of the first angle, and y be the measure of the second angle. We know that:
- x + y = 90 (since the angles are complementary)
- (x + y) - (x - y) = 86 (from the problem statement)
Substituting from the first equation into the second, we get:
90 - (x - y) = 86
This simplifies to:
90 - x + y = 86
90 - 86 = x - y
4 = x - y
So, we have two equations now:
- x + y = 90
- x - y = 4
Add these two equations together
2x = 94
x = 94/2
x = 47 degrees
Substituting x back into the first equation:
47 + y = 90
y = 90 - 47
y = 43 degrees
Therefore, the measures of the two angles are 47 degrees and 43 degrees.