Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

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Short Answer

Find the values $x$ of $y$ and

Values are $x = 30$ and $y = 5$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Label the given figure

Step 2. Observations from figure

Arrowheads denotes line segment $\bar{A B}, \bar{C D}$ , and $\bar{E F}$ are parallel

Line segment $\bar{B D}$ is transversal to the parallel lines $\bar{A B}, \bar{C D}$

Line segment $\bar{D F}$ is perpendicular to the parallel lines $\bar{C D}, \bar{E F}$

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

$∠ A B D$ and $∠ B D C$ 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.

$m ∠ A B C + m ∠ B D C = 180$

$70 + 4 x - 2 y = 180$

$4 x - 2 y = 180 - 70$

$4 x - 2 y = 110 (1)$

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

$∠ C D F$ and $∠ D F E$ 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.

$m ∠ C D F + m ∠ D F E = 180$

$4 x + 2 y + 50 = 180$

$4 x + 2 y = 180 - 50$

$4 x + 2 y = 130 (2)$

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

$4 x - 2 y = 110 4 x - 2 y = 130 8 x = 110 x = 30$

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

$4 (30) - 2 y = 110 - 2 y = 110 - 120 y = \frac{- 10}{- 2} y = 5$

Thus, $x = 30$ and $y = 5$

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Geometry

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Short Answer

Find the values $x$ of $y$ and

Step by Step Solution

Step 1. Label the given figure

Step 2. Observations from figure

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

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

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

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

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Geometry

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Short Answer

Find the values x of y and

Step by Step Solution

Step 1. Label the given figure

Step 2. Observations from figure

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

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

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

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

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