Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 7 - Similarity - Common Core Cumulative Standards Review - Selected Response - Page 486: 13


$x = 30$

Work Step by Step

We have a figure that is a parallelogram. Opposite angles of a parallelogram are congruent. We are given the measure of an exterior angle that is supplementary to this opposite angle. measure of interior angle = $180^{\circ} - 45^{\circ}$ Subtract to solve: measure of interior angle = $135^{\circ}$ We now know that the opposite angle is also $135^{\circ}$. Let's set the expression equal to this value to solve for $x$: $(4x + 15)^{\circ} = 135^{\circ}$ Subtract $15$ from each side of the equation to move constants to the right side of the equation: $4x = 120$ Divide both sides by $4$ to solve for $x$: $x = 30$
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