Why am I still not getting this one even after going back through websites and notes?
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?
College Algebra - bobpursley, Wednesday, November 18, 2009 at 9:47pm
A+B=90
A+ 1/4 * B =62.25
I would solve by subtracting the second equation from the first.
I would take Bob Pursley's suggestion.
That would leave you with
(3/4) B = 27.75
One more step, multiplying both sides by 4/3, will lead to the answer.
We are not going to do all the work for you.
To solve this problem, we can set up a system of equations based on the given information. Let's denote the measure of the first angle as A and the measure of the second angle as B.
From the problem statement, we know that the two angles are complementary, which means their sum is 90 degrees. So, our first equation is:
A + B = 90
We are also given that the sum of the measure of the first angle and one-fourth the second angle is 62.25 degrees. This gives us our second equation:
A + (1/4)B = 62.25
To solve this system of equations, we can use the substitution or elimination method. Let's use the elimination method in this case.
To eliminate the variable A, we can subtract the second equation from the first equation:
(A + B) - (A + (1/4)B) = 90 - 62.25
Simplifying this equation:
A + B - A - (1/4)B = 27.75
(4/4)B - (1/4)B = 27.75
(3/4)B = 27.75
To solve for B, we need to isolate it on one side of the equation. We can multiply both sides of the equation by the reciprocal of (3/4), which is (4/3):
(3/4)B * (4/3) = 27.75 * (4/3)
B = 37
Now that we have the value of B, we can substitute it back into either of the original equations to solve for A. Let's use the first equation:
A + B = 90
A + 37 = 90
A = 90 - 37
A = 53
So the measure of the smaller angle (A) is 53 degrees, and the measure of the other angle (B) is 37 degrees.
It's important to carefully read and understand the problem, identify the given information, and set up the appropriate equations. Solving the equations using the appropriate method and carefully performing the calculations will help you arrive at the correct answers.