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: 91


The measures of the three interior angles are $80{}^\circ ,50{}^\circ ,50{}^\circ $.

Work Step by Step

By using the angle sum property, the equation is obtained as follows: $x+2y=180{}^\circ $ (I) Since we know that one interior angle is y and one exterior angle is $2x-30$ and both lie on the same line, their sum is $180{}^\circ $ . The equation is obtained as: $\begin{align} & 2x-30+y=180{}^\circ \\ & 2x+y=210{}^\circ \end{align}$ (II) And to solve these equations, multiply equation (I) by $2$ and subtract equation (2): $\begin{align} & 3y=150{}^\circ \\ & y=50{}^\circ \end{align}$ And to obtain the value of x; put the value $y=50{}^\circ $ in either of the equations: $\begin{align} & x+2y=180 \\ & x+2\times 50=180 \\ & x+100=180 \\ & x=80{}^\circ \end{align}$ Hence, the measures of the interior angles are $80{}^\circ ,50{}^\circ ,50{}^\circ $.
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