Two angles are supplements if their sum is 180 degrees. The measure of one angle is seven-fifths the measure of its supplement. What is the measure of the sma

Question

Two angles are supplements if their sum is 180 degrees. The measure of one angle is seven-fifths the measure of its supplement. What is the measure of the smaller angle?

Answer 1

Hi Brandon for Yuba City, CA. Have a great day at school.

Great a Geometry problem. Great that you know the definition of a supplementary angle means. Make sure you know what a complementary angle also means.

So, you're trying to calculate the measure of the smaller angle

You are give that the measure of one of the angles is 7/5, which is 1 2/5 the measure of the other angle. Since these are supplementary angles, this means when we add the two angles together we will get 180°

So,                               angle 1 + angle 2  = 180°

  Label angle 1 and since we know it is 7/5 the other angle  =  (7/5)a

                                     and label angle 2     =  a

     Now your goal is to substitute the information into your equation:

                                 (7/5)a + a  =  180

This is how we set up the problem:

Now what happens next, we will need to add the 2 variable together, but one of them is a fraction. What do we need to do when adding a fraction?

HINT: I'll help you get started

                       7a   +   a     =    180        you will need to change the 

                        5                                   the a to a fraction

 

                       7a  +  5a = 180              Now we can rewrite our equation
                        5        5

 

                     7a  +  5a    =   180    Then complete the addition operation

                           5

 

                         12a        =    180     Now you need to solve for a

                           5

You should be able to continue and get an answer for a. 

I have solved it, but this is your problem. You will need to learn how to set up and complete these problems, because Wyzant will not be there when you are taking a test.

The answer I got satisfies the problem.

Try and solve it, if you need help, contact me on Wyzant. Once you get the skill to answer these problems, you will be a pro at them.

Answer 2

Let x = the smaller angle

Let (7/5)x = the larger angle

x + (7/5) x = 180

(12/5)x = 180      Multiply both sides by 5/7.

x = 75º

(7/5)(75) = 105º