Prealgebra (7th Edition)

Published by Pearson
ISBN 10: 0321955048
ISBN 13: 978-0-32195-504-3

Chapter 9 - Section 9.1 - Lines and Angles - Exercise Set: 73


$a = 60$ degrees $b = 50$ degrees $c = 110$ degrees $d = 70$ degrees $e = 120$ degrees

Work Step by Step

We know that adjacent angles sum to 180 degrees: $70+a+b = c+d = 60+e = 180$. From this, we know that $e=120$. From there, we know that opposite angles caused by two parallel lines and a transverse line are equal. Therefore, angles 70 degrees and $d$ are equal and angles 60 degrees and $a$ are equal. Therefore, $d = 70$ and $a = 60$. Finally, plugging $d$ and $a$ back into the first equation, we solve that $b = 50$ and $c = 110$.
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