Given that the two lines cut by the traversal are parallel, solve for the value of x below? 4x⁰ + 104° Leo the paperclip button below to attach filos
Given that the two lines cut by the traversal are parallel, solve for the value of x below? 4x⁰ + 104° Leo the paperclip button below to attach filos
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![**Problem Statement:**
Given that the two lines cut by the transversal are parallel, solve for the value of \( x \) below.
**Diagram Description:**
The diagram shows two parallel horizontal lines with a transversal line cutting through them, forming eight angles. The angles at the intersection of the transversal and the parallel lines are labeled with either given angles or expressions involving \( x \):
- One angle is labeled as \( 4x^\circ \).
- The corresponding angle on the other side of the transversal is labeled as \( 104^\circ \).
**Solution:**
Since the two lines are parallel, alternate interior angles are equal. Therefore, we can set the expressions for the angles equal to each other and solve for \( x \):
\[
4x = 104
\]
Divide both sides by 4:
\[
x = \frac{104}{4}
\]
\[
x = 26
\]
Hence, the value of \( x \) is \( 26 \) degrees.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe53cea77-c966-4d47-ae93-d2c22a57e8a1%2F618675a3-7f53-4681-8d3d-721366603940%2Fpq5av7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given that the two lines cut by the transversal are parallel, solve for the value of \( x \) below.
**Diagram Description:**
The diagram shows two parallel horizontal lines with a transversal line cutting through them, forming eight angles. The angles at the intersection of the transversal and the parallel lines are labeled with either given angles or expressions involving \( x \):
- One angle is labeled as \( 4x^\circ \).
- The corresponding angle on the other side of the transversal is labeled as \( 104^\circ \).
**Solution:**
Since the two lines are parallel, alternate interior angles are equal. Therefore, we can set the expressions for the angles equal to each other and solve for \( x \):
\[
4x = 104
\]
Divide both sides by 4:
\[
x = \frac{104}{4}
\]
\[
x = 26
\]
Hence, the value of \( x \) is \( 26 \) degrees.
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