I posted this early, I don't understand the answer, Two angles are complementary. The sum of the measure of the first angle and one-fourth the second angle is 87.75 degrees. Find the measures of the angles? What is the measure of the smaller angle? What is the measure of the other angle. Both in degrees...
Let x be the first angle, and y be the second angle.
The angles are complementary, so x + y = 90.
"The sum of the measure of the first angle and one-fourth the second angle is 87.75 degrees. "
x + y/4 = 87.75
To find the measures of the angles, let's start by assigning variables to the angles. Let's call the first angle x and the second angle y.
We know that two angles are complementary, which means their sum is 90 degrees. So we can write the equation:
x + y = 90 (Equation 1)
We are also given that the sum of the measure of the first angle and one-fourth the second angle is 87.75 degrees. Mathematically, we can write this as:
x + 1/4y = 87.75 (Equation 2)
Now we have a system of two equations. We can solve this system to find the values of x and y, which will give us the measures of the angles.
One way to solve this system is through substitution. From Equation 1, we can express x in terms of y by subtracting y from both sides:
x = 90 - y
We can substitute this value of x into Equation 2:
90 - y + 1/4y = 87.75
Now, we can solve for y:
90 - y + 1/4y = 87.75
-3/4y = -2.25
y = (-2.25)/(-3/4)
y = 3
So the second angle, y, measures 3 degrees.
Now, we can substitute the value of y back into Equation 1 to find x:
x + 3 = 90
x = 90 - 3
x = 87
Therefore, the measures of the angles are x = 87 degrees and y = 3 degrees.
The measure of the smaller angle is 3 degrees, and the measure of the other angle is 87 degrees.