Answer:
To solve this problem, let's represent the measure of the first angle as "x" and the measure of the second angle as "y".
According to the problem, one angle is 12 degrees less than four times the other angle. So we can write the equation:
x = 4y - 12
We are also told that the angles are complements of each other. Remember that complementary angles add up to 90 degrees. So we can write the equation:
x + y = 90
Now we have a system of equations. We can solve it by substitution or elimination.
Let's solve it by substitution.
We know from the first equation that x = 4y - 12. We can substitute this value of x into the second equation:
(4y - 12) + y = 90
Combining like terms, we get:
5y - 12 = 90
Adding 12 to both sides, we have:
5y = 102
Dividing both sides by 5, we get:
y = 20.4
But since the angles are in degrees, we need to round this to the nearest whole number. So y is approximately 20.
Now, we can substitute this value of y back into the first equation to find x:
x = 4(20) - 12
x = 80 - 12
x = 68
So the two angles are approximately 68 degrees and 20 degrees.
But wait! Are these angles complements of each other? Let's check:
68 + 20 = 88
It seems like they are not complements of each other. Therefore, the given answers of 27, 72, and 81 are incorrect.
In conclusion, based on the given information, there doesn't seem to be a solution where the angles are complements of each other. No real solution.
Explanation: