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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 3: Q10 (page 81)

Find the values of $x$ and $y$

Short Answer

Expert verified

Values are $x = 70$ and role="math" localid="1637745946360" $y = 60$

Step by step solution

01

Step 1. Label the given figure

02

Step 2. Observations from figure

Arrowheads denotes line segment $\bar{A B}$ is parallel to $\bar{C D}$

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

03

Step 3. Find x degree

$∠ G E A$ and $∠ E C D$ forms a pair of corresponding angles

Postulate 10: If two parallel lines are cut by a transversal then the corresponding angles are congruent

$∠ G E A ≅ ∠ E C D$

$x = m ∠ E C D$

Thus,

04

Step 4. Find y degree

$∠ A E D$ and $∠ F E B$ forms a pair of vertically opposite angles

$∠ A E D ≅ ∠ F E B$

$m ∠ A E D = m ∠ F E B$

$m ∠ A E D = 50$

Since, $∠ G E A, ∠ A E D$ , and $∠ D E C$ forms the straight line $\bar{G C}$ so these angles are supplementary angles. That is,

$m ∠ G E A + m ∠ A E D + m ∠ D E C = 180$

$70 + 50 + y = 180$

$120 + y = 180$

role="math" localid="1637746929112" $y = 180 - 120$

$y = 60$

Thus $y = 60$

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Most popular questions from this chapter

If $a ∥ b$ , name all angels that must be congruent to $∠ 1$ .

Find the values $x$ of $y$ and

Classify each pair of angles as alternate interior angles, same-side interior angles, corresponding angles, or none of these.

and

Name five lines parallel to plane ABCD

Draw each figure described.

42. Lines I $∥$ plane X, plane X $∥$ plane Y, and I is not parallel to Y.

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