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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: Q8 (page 81)

Find the values of $x$ and $y$

Short Answer

Expert verified

Values are $x = 10$ and $y = 45$

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 $\bar{D C}$

Line segments $\bar{B C}$ and $\bar{A D}$ are transversal to these parallel lines

03

Step 3. Find x degree

$∠ B A D$ and $∠ A D C$ 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.

$\begin{matrix} m ∠ B A D + m ∠ A D C = 180 \\ 4 x + 14 x = 180 \\ 18 x = 180 \\ x = \frac{180}{18} \end{matrix}$

Thus, $x = 10$

04

Step 4. Find y degree

$∠ D C B$ and $∠ C B A$ 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.

$\begin{matrix} m ∠ D C B + m ∠ C B A = 180 \\ 2 y + 90 = 180 \end{matrix}$

$\begin{matrix} 2 y = 180 - 90 \\ y = \frac{90}{2} \end{matrix}$

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Most popular questions from this chapter

State the postulate or theorem that justifies each statement.

$m ∠ 4 = m ∠ 8$

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

and

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

and

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

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

Two lines that are not coplanar intersect.

See all solutions

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