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Given: m %3D

Given: m %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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**Geometry Question from Final Exam** **Question 15:** Given: - \( m \angle X = 110^\circ \) - \( WZ \cong YZ \) - \( m \angle Y = 100^\circ \) Refer to the diagram to find the measure of each of the following: a. \( \angle Z \) b. \( \overline{WZ} \) c. \( \angle W \) d. \( \overline{WX} \) **Diagram Explanation:** The diagram presented is a cyclic quadrilateral \( WXYZ \) inscribed in a circle. Here are the detailed features of the diagram: - Points \( W, X, Y, \) and \( Z \) lie on the circumference of the circle. - Each side of the quadrilateral is a chord of the circle. - Two sides of the quadrilateral, \( WZ \) and \( YZ \), are marked with congruence symbols (indicating they are of equal length). - The angles of the quadrilateral are labeled at each vertex: \( \angle X, \angle Y, \angle Z, \) and \( \angle W \). **Note for students:** When solving this problem, consider properties of cyclic quadrilaterals, such as opposite angles summing to \( 180^\circ \), and congruent sides to identify the measures of unknown components in the figure.
Transcribed Image Text:**Geometry Question from Final Exam** **Question 15:** Given: - \( m \angle X = 110^\circ \) - \( WZ \cong YZ \) - \( m \angle Y = 100^\circ \) Refer to the diagram to find the measure of each of the following: a. \( \angle Z \) b. \( \overline{WZ} \) c. \( \angle W \) d. \( \overline{WX} \) **Diagram Explanation:** The diagram presented is a cyclic quadrilateral \( WXYZ \) inscribed in a circle. Here are the detailed features of the diagram: - Points \( W, X, Y, \) and \( Z \) lie on the circumference of the circle. - Each side of the quadrilateral is a chord of the circle. - Two sides of the quadrilateral, \( WZ \) and \( YZ \), are marked with congruence symbols (indicating they are of equal length). - The angles of the quadrilateral are labeled at each vertex: \( \angle X, \angle Y, \angle Z, \) and \( \angle W \). **Note for students:** When solving this problem, consider properties of cyclic quadrilaterals, such as opposite angles summing to \( 180^\circ \), and congruent sides to identify the measures of unknown components in the figure.
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