College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 5 - Systems of Equations and Inequalities - Exercise Set 5.1 - Page 531: 84

Answer

$x = 30$ degrees; $y = 75$ degrees

Work Step by Step

The sum of all interior angles in a triangle equals 180 degrees. Also, adjacent angles on a straight line also add up to 180 degrees. This means that we can write the following system of equations: $$x + 2y = 180$$ $$3x + 15 + y = 180$$ which is to say: $$x + 2y = 180$$ $$3x + y = 165$$ We can use the substitution method to find the equivalent value of one of the variables: $$x + 2y = 180$$ $$x = 180 - 2y$$ and plug this value into the other equation: $$3x + y = 165$$ $$3(180 - 2y) + y = 165$$ $$540 - 6y + y = 165$$ $$375 = 5y$$ $$75 = y$$ We now substitute this value into the previous equation: $$x = 180 - 2y$$ $$x = 180 - 2(75) = 180 - 150 = 30$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.