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find the value of x, y and z. 200 35° 95° 110° %3D

find the value of x, y and z. 200 35° 95° 110° %3D

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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**Find the Values of x, y, and z** In this exercise, we are given a diagram consisting of a circle and several angles associated with different arcs and lines intersecting at various points. You are required to determine the values of the angles labeled as \( x \), \( y \), and \( z \) based on the given information. **Diagram Breakdown:** 1. **Circle:** - Inside the circle, one of the central angles is labeled as \( 110^\circ \). - Another angle inscribed in the circle is represented as \( x^\circ \) opposite to the \( 110^\circ \) angle. 2. **External Angles and Lines:** - There is an external angle \( 95^\circ \) that intersects the circle at two points, creating two arcs. - An angle of \( 20^\circ \) and an angle of \( 35^\circ \) are also present, forming additional intersections outside the circle leading to the angle labeled as \( z^\circ \). - The angle \( y^\circ \) is formed by extending one of the lines intercepting the circle's boundary. **Values to Determine:** - \( x = \) - \( y = \) - \( z = \) Using your knowledge of circle theorems and angle properties, calculate the values of \( x \), \( y \), and \( z \).
Transcribed Image Text:**Find the Values of x, y, and z** In this exercise, we are given a diagram consisting of a circle and several angles associated with different arcs and lines intersecting at various points. You are required to determine the values of the angles labeled as \( x \), \( y \), and \( z \) based on the given information. **Diagram Breakdown:** 1. **Circle:** - Inside the circle, one of the central angles is labeled as \( 110^\circ \). - Another angle inscribed in the circle is represented as \( x^\circ \) opposite to the \( 110^\circ \) angle. 2. **External Angles and Lines:** - There is an external angle \( 95^\circ \) that intersects the circle at two points, creating two arcs. - An angle of \( 20^\circ \) and an angle of \( 35^\circ \) are also present, forming additional intersections outside the circle leading to the angle labeled as \( z^\circ \). - The angle \( y^\circ \) is formed by extending one of the lines intercepting the circle's boundary. **Values to Determine:** - \( x = \) - \( y = \) - \( z = \) Using your knowledge of circle theorems and angle properties, calculate the values of \( x \), \( y \), and \( z \).
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