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Given m | n, find the value of x and y. m (4x-2)° yo (6x+12)°

Given m | n, find the value of x and y. m (4x-2)° yo (6x+12)°

Elementary Geometry For College Students, 7e
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
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**Problem:** Given \( m \parallel n \), find the values of \( x \) and \( y \). **Diagram Explanation:** - The diagram shows two parallel lines \( m \) and \( n \) intersected by a transversal. - One of the angles formed on line \( m \) by the transversal is labeled as \( (4x - 2)^\circ \). - The corresponding angle on line \( n \) is labeled as \( y^\circ \). - Another angle on line \( n \), adjacent to the angle \( y^\circ \), is labeled as \( (6x + 12)^\circ \). **Solution Approach:** 1. **Corresponding Angles:** - Since lines \( m \) and \( n \) are parallel, the corresponding angles are equal. Therefore, \( (4x - 2)^\circ = y^\circ \). 2. **Linear Pair:** - Angles \( y^\circ \) and \( (6x + 12)^\circ \) are linear pairs, hence they sum up to \( 180^\circ \). Therefore, \( y + (6x + 12) = 180 \). This setup allows us to solve the equations to find the values of \( x \) and \( y \).
Transcribed Image Text:**Problem:** Given \( m \parallel n \), find the values of \( x \) and \( y \). **Diagram Explanation:** - The diagram shows two parallel lines \( m \) and \( n \) intersected by a transversal. - One of the angles formed on line \( m \) by the transversal is labeled as \( (4x - 2)^\circ \). - The corresponding angle on line \( n \) is labeled as \( y^\circ \). - Another angle on line \( n \), adjacent to the angle \( y^\circ \), is labeled as \( (6x + 12)^\circ \). **Solution Approach:** 1. **Corresponding Angles:** - Since lines \( m \) and \( n \) are parallel, the corresponding angles are equal. Therefore, \( (4x - 2)^\circ = y^\circ \). 2. **Linear Pair:** - Angles \( y^\circ \) and \( (6x + 12)^\circ \) are linear pairs, hence they sum up to \( 180^\circ \). Therefore, \( y + (6x + 12) = 180 \). This setup allows us to solve the equations to find the values of \( x \) and \( y \).
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