Geometry: Common Core (15th Edition)

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

Chapter 6 - Polygons and Quadrilaterals - 6-3 Proving That a Quadrilateral Is a Parallelogram - Practice and Problem-Solving Exercises - Page 374: 33


$m = 12$ $x = 15$

Work Step by Step

In parallelograms, opposite sides are congruent, so let's set the expressions for opposite sides equal to one another to solve for $m$: $m + 7 = 3m - 17$ $m = 3m - 24$ Subtract $3m$ from both sides of the equation to isolate the variable on the left side of the equation: $-2m = -24$ Divide each side by $-2$ to solve for $m$: $m = 12$ In parallelograms, consecutive angles are supplementary, so let's set the sum of the expressions for the two consecutive angles equal to $180$: $3x + (8x + 15) = 180$ Combine like terms: $11x + 15 = 180$ Subtract $15$ from each side of the equation to isolate constants on the right side of the equation: $11x = 165$ Divide both sides of the equation by $11$ to solve for $x$: $x = 15$
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