Geometry: Common Core (15th Edition)

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

Chapter 5 - Relationships Within Triangles - Chapter Test - Page 345: 13


$x = 7$

Work Step by Step

One angle in the two triangles is marked congruent. The adjacent angles are also congruent because they are both right angles, and right angles are congruent. We have two congruent triangles. One side is congruent because it is shared by both triangles. Therefore, these two triangles are congruent by AAS. Corresponding parts of congruent triangles are congruent; therefore, we can set the two sides whose expressions are given equal to one another: $5x - 8 = 2x + 13$ Subtract $2x$ from each side of the equation to move variables to the left side of the equation: $3x - 8 = 13$ Add $8$ to each side of the equation to move constants to the right side of the equation: $3x = 21$ Divide each side by $3$ to solve for $x$: $x = 7$
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