Consider the figure below in which 4₁ || 1₂, mza = 13y, m/b = 31y+4, m

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
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Consider the Figure Below

**Question:**

Consider the figure below in which \( l_1 \parallel l_2 \). \( m\angle a = 13y \), \( m\angle b = 31y + 4 \), \( m\angle r = 30x + 40 \), and \( m\angle s = 130x - 160 \).

[Diagram Description:]

- The figure shows two parallel lines \( l_1 \) and \( l_2 \).
- There are two transversals, \( t_1 \) and \( t_2 \), intersecting these parallel lines.
- The angles formed at the intersections are labeled as follows:
  - \( \angle a \) at the intersection of \( t_1 \) and \( l_1 \).
  - \( \angle b \) at the intersection of \( t_2 \) and \( l_2 \).
  - \( \angle r \) between \( l_1 \) and \( l_2 \), adjacent to both transversals on the top.
  - \( \angle s \) between \( l_1 \) and \( l_2 \), adjacent to both transversals on the bottom.

**Problem:**

What are the values of \( \angle a \), \( \angle b \), \( \angle r \), and \( \angle s \)?

**Spaces for Answers:**

\[
\begin{align*}
\angle a &= \, \underline{\hspace{2cm}} \\
\angle b &= \, \underline{\hspace{2cm}} \\
\angle r &= \, \underline{\hspace{2cm}} \\
\angle s &= \, \underline{\hspace{2cm}} \\
\end{align*}
\]

**Answer:**

[Answer content would be provided here based on solving the equations.]
Transcribed Image Text:**Question:** Consider the figure below in which \( l_1 \parallel l_2 \). \( m\angle a = 13y \), \( m\angle b = 31y + 4 \), \( m\angle r = 30x + 40 \), and \( m\angle s = 130x - 160 \). [Diagram Description:] - The figure shows two parallel lines \( l_1 \) and \( l_2 \). - There are two transversals, \( t_1 \) and \( t_2 \), intersecting these parallel lines. - The angles formed at the intersections are labeled as follows: - \( \angle a \) at the intersection of \( t_1 \) and \( l_1 \). - \( \angle b \) at the intersection of \( t_2 \) and \( l_2 \). - \( \angle r \) between \( l_1 \) and \( l_2 \), adjacent to both transversals on the top. - \( \angle s \) between \( l_1 \) and \( l_2 \), adjacent to both transversals on the bottom. **Problem:** What are the values of \( \angle a \), \( \angle b \), \( \angle r \), and \( \angle s \)? **Spaces for Answers:** \[ \begin{align*} \angle a &= \, \underline{\hspace{2cm}} \\ \angle b &= \, \underline{\hspace{2cm}} \\ \angle r &= \, \underline{\hspace{2cm}} \\ \angle s &= \, \underline{\hspace{2cm}} \\ \end{align*} \] **Answer:** [Answer content would be provided here based on solving the equations.]
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