# Chapter 6 - Polygons and Quadrilaterals - 6-3 Proving That a Quadrilateral Is a Parallelogram - Practice and Problem-Solving Exercises - Page 372: 11

$x = 5$

#### Work Step by Step

Parallelograms have opposite sides that are congruent. In order for $ABCD$ to be a parallelogram, we must have $AB$ and $CD$ equal to one another. $AB = CD$ Let's plug in what we are given in the diagram: $5x - 8 = 2x + 7$ Add $8$ to each side of the equation to isolate variables on one side of the equation: $5x = 2x + 15$ Subtract $2x$ from each side of the equation to isolate the variable on the left side of the equation: $3x = 15$ Divide each side of the equation by $3$ to solve for $x$: $x = 5$

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