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Find the values of x and y . 4x (7y – 12)° (бу + 8)(6х — 26)°

Find the values of x and y . 4x (7y – 12)° (бу + 8)(6х — 26)°

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 Statement:** Find the values of \( x \) and \( y \). **Diagram Explanation:** The diagram presents two intersecting lines, creating four angles. The angles are expressed in terms of \( x \) and \( y \): - The top left angle is labeled \( 4x^\circ \). - The top right angle is labeled \( (7y - 12)^\circ \). - The bottom left angle is labeled \( (6y + 8)^\circ \). - The bottom right angle is labeled \( (6x - 26)^\circ \). **Solution Approach:** 1. **Identify Vertical Angles:** - Vertical angles are equal. Thus, the angles \( 4x^\circ \) and \( (6x - 26)^\circ \) are vertical and equal. - Set the equation: \[ 4x = 6x - 26 \] 2. **Solve for \( x \):** - Rearrange and solve: \[ 4x = 6x - 26 \] \[ 26 = 6x - 4x \] \[ 26 = 2x \] \[ x = 13 \] 3. **Identify Additional Vertical Angles:** - Similarly, angles \( (7y - 12)^\circ \) and \( (6y + 8)^\circ \) are vertical and therefore equal. - Set the equation: \[ 7y - 12 = 6y + 8 \] 4. **Solve for \( y \):** - Rearrange and solve: \[ 7y - 12 = 6y + 8 \] \[ 7y - 6y = 8 + 12 \] \[ y = 20 \] **Conclusion:** The values of \( x \) and \( y \) are \( x = 13 \) and \( y = 20 \) respectively.
Transcribed Image Text:**Problem Statement:** Find the values of \( x \) and \( y \). **Diagram Explanation:** The diagram presents two intersecting lines, creating four angles. The angles are expressed in terms of \( x \) and \( y \): - The top left angle is labeled \( 4x^\circ \). - The top right angle is labeled \( (7y - 12)^\circ \). - The bottom left angle is labeled \( (6y + 8)^\circ \). - The bottom right angle is labeled \( (6x - 26)^\circ \). **Solution Approach:** 1. **Identify Vertical Angles:** - Vertical angles are equal. Thus, the angles \( 4x^\circ \) and \( (6x - 26)^\circ \) are vertical and equal. - Set the equation: \[ 4x = 6x - 26 \] 2. **Solve for \( x \):** - Rearrange and solve: \[ 4x = 6x - 26 \] \[ 26 = 6x - 4x \] \[ 26 = 2x \] \[ x = 13 \] 3. **Identify Additional Vertical Angles:** - Similarly, angles \( (7y - 12)^\circ \) and \( (6y + 8)^\circ \) are vertical and therefore equal. - Set the equation: \[ 7y - 12 = 6y + 8 \] 4. **Solve for \( y \):** - Rearrange and solve: \[ 7y - 12 = 6y + 8 \] \[ 7y - 6y = 8 + 12 \] \[ y = 20 \] **Conclusion:** The values of \( x \) and \( y \) are \( x = 13 \) and \( y = 20 \) respectively.
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