Geometry: Common Core (15th Edition)

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

Chapter 6 - Polygons and Quadrilaterals - 6-2 Properties of Parallelograms - Lesson Check - Page 363: 3


$x = 5$

Work Step by Step

The diagram is that of a parallelogram. Opposite sides of a parallelogram are congruent. We see that $\overline{AB}$ and $\overline{DC}$ are opposite sides. Let's set $AB$ and $DC$ equal to one another so we can solve for $x$: $AB = DC$ Let's plug in what we know: $x + 2 = 2x - 3$ Subtract $2$ from each side of the equation to isolate constants on one side: $x = 2x - 5$ Subtract $2x$ from each side of the equation to isolate the variable on one side of the equation: $-x = -5$ Divide both sides by $-1$ to solve for $x$: $x = 5$
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