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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: Q11 (page 81)

Find the values of $x$ and $y$

Short Answer

Expert verified

Values are $x = 14$ and $y = 9$

Step by step solution

01

Step 1. Label the given figure

02

Step 2. Observations from figure

Arrowheads denote line segment $\bar{A B}$ is parallel to $\bar{X Y}$

Line segments $\bar{Y B}, \bar{X B}, and \bar{X A}$ are transversal to the parallel lines

03

Step 3. Find x degree

$∠ Y X B$ and $∠ X B A$ forms a pair of alternate interior angles

Theorem 3-2: If two parallel lines are cut by a transversal then the alternate interior angles are congruent.

$\begin{matrix} ∠ X B A ≅ ∠ Y X B \\ m ∠ X B A = m ∠ E C D \\ 3 x = 42 \\ x = \frac{42}{3} \\ x = 14 \end{matrix}$

Thus, $x = 14$

04

Step 4. Find y degree

$90 + 6 y - 6 + 3 x = 180$ $∠ X Y B$ and $∠ Y B A$ 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.

$m ∠ X Y B + m ∠ Y B A = 180$

$90 + 6 y - 6 + 3 x = 180$

$84 + 6 y + (3 \times 14) = 180$

$6 y = 180 - 84 - 42$

$y = \frac{54}{6}$

$y = 9$

Thus $y = 9$

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Most popular questions from this chapter

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

and

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

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Prove $\vec{S A}$ bisects $∠ B S R$

Assume that $a ∥ b$ and $c ∥ d$ , name all angels congruent to $∠ 2$ .

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

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