I have tried this problem a few ways, and I am getting frustrating results. Could you help me out by showing me how to set the systems of equations
Two angles are complementary The sum of the measure of the first angle and 1/4 the second angle is 82.5. Find the measure of the angles.
I think that the first equation will look like this: x+y=90, but I am stuck on the set up of the second one.
second equation:
x + (1/4)y = 82.5
multiply by 4
4x + y = 330
now subtract the first from the second
4x + y = 330
x + y = 90
------------
3x = 240
x = 80
so one is 80 degrees, the other 10 degrees.
To set up the second equation, let's assign variables to the angles.
Let's say the first angle is x degrees and the second angle is y degrees.
According to the problem, the two angles are complementary, which means their measures add up to 90 degrees. So, the first equation is correct: x + y = 90.
Now, let's set up the second equation using the information given in the problem. It states that the sum of the measure of the first angle and 1/4 the second angle is 82.5.
Using the variables we assigned, the equation is: x + (1/4)y = 82.5.
This equation represents the information that the sum of the measure of the first angle (x degrees) and 1/4 the measure of the second angle (1/4 * y degrees) is equal to 82.5 degrees.
Now, you have a system of equations:
Equation 1: x + y = 90
Equation 2: x + (1/4)y = 82.5
To solve this system, you can use various methods such as substitution, elimination, or graphing. Pick the method you prefer or are most comfortable with and solve for the values of x and y.