Geometry: Common Core (15th Edition)

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

Chapter 5 - Relationships Within Triangles - Common Core Cumulative Standards Review - Selected Response - Page 348: 11

Answer

$x = 3$

Work Step by Step

These two angles are same-side exterior angles, meaning they lie on the same side of the transversal but outside of the parallel lines. Same-side exterior angles are supplementary, so we can add the two angles together and set them equal to $180^{\circ}$. $(\frac{3x - 4}{2}) + (4x + \frac{x}{2} + 2) = 180$ $\frac{3x - 4}{2} + \frac{8x}{2} + \frac{x}{2} + 2 = 180$ $\frac{3x - 4 + 8x + x}{2} + 2 = 180$ Combine like terms: $\frac{12x - 4}{2} + 2 = 180$ Simplify the fraction by dividing both the numerator and denominator by their greatest common denominator, $2$: $6x - 2 + 2 = 180$ Combine like terms: $6x = 180$ Divide both sides by $6$ to solve for $x$: $x = 30$
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