Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 1 - Section 1.4 - Further Applications of Linear Equations - 1.4 Exercises: 33

Answer

$(7x+17)^o=122^o ,\\ (8x+2)^o=122^o$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Equate the given vertical angles, and use the properties of equality to isolate $x.$ Then substitute the value of $x$ in the following given vertical angles: \begin{array}{l}\require{cancel} (7x+17)^o ,\\ (8x+2)^o .\end{array} $\bf{\text{Solution Details:}}$ Since vertical angles have the same measure, then \begin{array}{l}\require{cancel} 7x+17=8x+2 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} 7x-8x=2-17 \\\\ -x=-15 \\\\ x=15 .\end{array} Substituting $x= 15 $ in the angle $ (7x+17)^o $ results to \begin{array}{l}\require{cancel} (7\cdot15+17)^o \\\\= (105+17)^o \\\\= 122^o .\end{array} Substituting $x= 15 $ in the angle $ (8x+2)^o $ results to \begin{array}{l}\require{cancel} (8\cdot15+2)^o \\\\= (120+2)^o \\\\= 122^o .\end{array} Hence, the measures of the vertical angles are \begin{array}{l}\require{cancel} (7x+17)^o=122^o ,\\ (8x+2)^o=122^o .\end{array}
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