I posted this early, I don't understand, 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 A = first angle and B = second
A + .25B = 87.75
A + B = 90 (complementary)
A = 90 - B
Substitute 90 - B for A in the first equation to find B. Substitute B into the second equation to find A. Check by putting both values into the first equation.
To find the measures of the two angles, let's represent them as variables. Let's call the first angle x and the second angle y.
We are given that the angles are complementary, which means their measures add up to 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 represent this information as:
x + (1/4)y = 87.75 (Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) that we can solve simultaneously to find the values of x and y.
One way to solve this system of equations is by substitution. We can solve Equation 1 for x and substitute it into Equation 2.
From Equation 1, we have:
x = 90 - y
Substituting this into Equation 2, we get:
(90 - y) + (1/4)y = 87.75
Now, we can solve this equation for y:
90 - y + (1/4)y = 87.75
Multiplying through by 4 to eliminate the fraction:
360 - 4y + y = 351
Combining like terms:
360 - 3y = 351
Subtracting 360 from both sides:
-3y = -9
Dividing by -3:
y = 3
Now that we have y = 3, we can substitute this value 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 smaller angle is 3 degrees, and the other angle is 87 degrees.