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Expert-verified Found in: Page 82 ### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279 # Find the values $x$ of $y$ and Values are $\mathbit{x}\mathbf{=}\mathbf{30}$ and $\mathbit{y}\mathbf{=}\mathbf{5}$

See the step by step solution

## Step 1. Label the given figure ## Step 2. Observations from figure

Arrowheads denotes line segment $\overline{AB},\overline{CD}$, and $\overline{EF}$ are parallel

Line segment $\overline{BD}$ is transversal to the parallel lines $\overline{AB},\overline{CD}$

Line segment $\overline{DF}$ is perpendicular to the parallel lines $\overline{CD},\overline{EF}$

## Step 3. Find first relation between x degree and y degree

$\angle ABD$ and $\angle BDC$ forms a pair of same-side interior angles

Theorem 3-3: If two parallel lines are cut by a transversal then the same-side interior angles are supplementary.

$m\angle ABC+m\angle BDC=180$

$70+4x-2y=180$

$4x-2y=180-70$

$4x-2y=110\text{}\left(1\right)$

## Step 4. Find second relation between x degree and y degree

$\angle CDF$ and $\angle DFE$ forms a pair of same-side interior angles

Theorem 3-3: If two parallel lines are cut by a transversal then the same-side interior angles are supplementary.

$m\angle CDF+m\angle DFE=180$

$4x+2y+50=180$

$4x+2y=180-50$

$4x+2y=130\text{}\left(2\right)$

## Step 5. Add equations (1) and (2)

$4x-2y=110\phantom{\rule{0ex}{0ex}}\overline{)4x-2y=130}\phantom{\rule{0ex}{0ex}}8x=110\phantom{\rule{0ex}{0ex}}x=30$

## Step 6. Substitute 30 for x in equation (1)

$4\left(30\right)-2y=110\phantom{\rule{0ex}{0ex}}-2y=110-120\phantom{\rule{0ex}{0ex}}y=\frac{-10}{-2}\phantom{\rule{0ex}{0ex}}y=5$

Thus, $x=30$ and $y=5$ ### Want to see more solutions like these? 