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Given the figure belo find the values of x and z. (10x + 3) (5x + 53)°

Given the figure belo find the values of x and z. (10x + 3) (5x + 53)°

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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**Question 4** Given the figure below, find the values of \( x \) and \( z \). *Diagram Description:* The diagram shows two intersecting lines, forming two pairs of vertically opposite angles. - One angle is labeled as \((10x + 3)^\circ\). - The vertically opposite angle is labeled as \((5x + 53)^\circ\). - An adjacent angle is labeled as \(z^\circ\). The task is to determine the values of \( x \) and \( z \) using properties of vertical and supplementary angles. The basic mathematical principles to apply are: 1. Vertically opposite angles are equal. 2. The sum of angles forming a straight line is \(180^\circ\). Use these properties to set up equations that can be solved to find \( x \) and \( z \).
Transcribed Image Text:**Question 4** Given the figure below, find the values of \( x \) and \( z \). *Diagram Description:* The diagram shows two intersecting lines, forming two pairs of vertically opposite angles. - One angle is labeled as \((10x + 3)^\circ\). - The vertically opposite angle is labeled as \((5x + 53)^\circ\). - An adjacent angle is labeled as \(z^\circ\). The task is to determine the values of \( x \) and \( z \) using properties of vertical and supplementary angles. The basic mathematical principles to apply are: 1. Vertically opposite angles are equal. 2. The sum of angles forming a straight line is \(180^\circ\). Use these properties to set up equations that can be solved to find \( x \) and \( z \).
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