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 373: 24


$x = 24$

Work Step by Step

If two lines are cut by a transversal and alternate interior angles are congruent, then those lines are parallel. Let's set the two angles equal to one another: $m \angle BAC = m \angle DCA$ Plug in our knowns from the diagram: $2x + 15 = 4x - 33$ Subtract $15$ from each side of the equation to move constants to the right side of the equation: $2x = 4x - 48$ Subtract $4x$ from each side of the equation to move the variable to the left side of the equation: $-2x = -48$ Divide both sides of the equation by $-2$ to solve for $x$: $x = 24$
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