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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: Q9 (page 81)

Find the values of $x$ and $y$

Short Answer

Expert verified

Values are $x = 60$ and $y = 18$

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 $\bar{A C}$

Double arrowheads denotes line segment $\bar{H E}$ is parallel to $\bar{F G}$

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

Line segment $\bar{F D}$ is transversal to parallel lines $\bar{H E}$ and $\bar{F G}$ .

03

Step 3. Find x degree

$∠ B A H$ and $∠ B A E$ forms a linear pair, so sum of these angles is supplementary

$m ∠ B A H + m ∠ B A E = 180$

$120 + m ∠ B A E = 180$

$m ∠ B A E = 180 - 120$

$m ∠ B A E = 60$

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

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

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Most popular questions from this chapter

Classify each pair of angles as alternate interior, same side interior or corresponding angles

art

and

Complete each statement with the word always, sometimes, or never.

Two planes parallel to the same line are parallel to each other

Find the values $x$ of $y$ and

Name the two lines and the transversal that form each pair of angles.

and

State the postulate or theorem that justifies each statement.

$∠ 3$ is supplementary to $∠ 5$

See all solutions

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