Please explain in detail so I know for next time.
Two angles are complementary. The sum of the measure of the first angle and one-fourth the second angle is 62.25 degrees. Find the measures of the angles.
What is the measure of the smaller angle?
What is the measure of the other angle?
A+B=90
A+ 1/4 * B =62.25
I would solve by subtracting the second equation from the first.
This site may help you figure this problem out yourself.
http://www.mathsisfun.com/geometry/complementary-angles.html
To solve this problem, we need to use the information given and set up equations to find the measures of the angles.
Let's denote the measure of the first angle as x degrees and the measure of the second angle as y degrees.
According to the problem, the two angles are complementary, which means that their sum is equal to 90 degrees. Thus, we have 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 (y/4) is equal to 62.25 degrees. This gives us another equation:
x + y/4 = 62.25 --- Equation 2
To solve this system of equations, we can use substitution or elimination method. Let's use substitution method in this case.
From Equation 1, we can solve for x:
x = 90 - y
Substituting this into Equation 2, we get:
90 - y + y/4 = 62.25
Now, we can solve this equation for y:
Multiplying both sides by 4, we get:
360 - 4y + y = 249
Combining like terms:
360 - 3y = 249
Subtracting 360 from both sides:
-3y = -111
Dividing both sides by -3:
y = 37
Now that we have found the value of y (the measure of the second angle), we can substitute it back into Equation 1 to find the value of x (the measure of the first angle):
x + y = 90
x + 37 = 90
Subtracting 37 from both sides:
x = 90 - 37
x = 53
Therefore, the measure of the smaller angle is 53 degrees, and the measure of the other angle is 37 degrees.
To summarize:
- The smaller angle measures 53 degrees.
- The other angle measures 37 degrees.