Geometry: Common Core (15th Edition)

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

Chapter 6 - Polygons and Quadrilaterals - Common Core Cumulative Standards Review - Selected Response - Page 427: 8



Work Step by Step

A transversal intersects the parallel lines $g$ and $h$. Therefore, same-side interior angles are supplementary. The angles whose measures are given by expressions in the diagram are same-side interior angles; therefore, we can add these expressions together and set them equal to $180^{\circ}$ to find the value of $x$: $(2x + 10) + (5x - 5) = 180$ Group like terms together on the left side of the equation: $(2x + 5x) + (10 - 5) = 180$ Combine like terms to simplify: $(7x) + (5) = 180$ Subtract $5$ from each side of the equation to move constants to the right side of the equation: $7x = 175$ Divide each side of the equation by $7$ to solve for $x$: $x = 25$ This corresponds to answer option $I$.
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