Final answer:
Two complementary angles can be found by solving a system of equations. One angle is 82.25 degrees and the other angle is 11.75 degrees.
Step-by-step explanation:
Let's call one angle x and the other angle y.
We know that the two angles are complementary, which means they add up to 90 degrees.
We also know that one angle is 4 less than 7 times the other.
So, we can write the following equation: x + y = 90 and x = (7y) - 4.
Solving these two equations simultaneously, we can find the values of x and y. Substituting x in the first equation, we have (7y) - 4 + y = 90.
Combining like terms, we get:
8y - 4 = 90
Adding 4 to both sides, we get:
8y = 94
Dividing both sides by 8, we get:
y = 11.75
Substituting the value of y back into the second equation, we get:
x = (7 * 11.75) - 4 = 82.25
So, the measure of one angle is 82.25 degrees and the measure of the other angle is 11.75 degrees.