Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 7 - Section 7.1 - Systems of Linear Equations in Two Variables - Exercise Set - Page 823: 92


The measures of the three interior angles are $75{}^\circ ,75{}^\circ ,30{}^\circ $.

Work Step by Step

By using angle sum property, the equation is obtained as follows: $x+2y=180{}^\circ $ (I) We know that one interior angle is y and one exterior angle is $3x+15$ and both lie on the same line; thus, their sum is $180{}^\circ $. And the equation is obtained as: $\begin{align} & 3x+15+y=180{}^\circ \\ & 3x+y=165{}^\circ \end{align}$ (II) And to solve these equations, multiply equation (I) by $3$ and subtract equation (II): $\begin{align} & 5y=375{}^\circ \\ & y=75{}^\circ \end{align}$ And to obtain the value of x, substitute the value $y=75{}^\circ $ in either of the equations: $\begin{align} & x+2\left( 75 \right)=180{}^\circ \\ & x=30{}^\circ \end{align}$ Hence, the measures of the interior angles are $75{}^\circ ,75{}^\circ ,30{}^\circ $.
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