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5. Find mCDE D C E B F 20° A

5. Find mCDE D C E B F 20° A

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 Problem: Finding the Measure of Angle CDE #### Problem Statement: 5. Find the measure of angle \( \angle CDE \). #### Diagram Description: - The given diagram is a circle with center at point \( B \). - The circle is intersected by several lines. - Points \( C \), \( D \), and \( E \) are marked on the circumference such that \( C \), \( D \), and \( E \) form part of a closed path. - Point \( A \) also lies on the circumference, with line segment \( FA \) making a 20° angle with line segment \( BA \). - There is a right angle (90°) shown at point \( B \). In the diagram: - \( BE \) extends from the center \( B \) to the circumference at point \( E \). - \( BD \) extends from the center \( B \) to the circumference at point \( D \). - \( BA \) also extends from the center \( B \) to the circumference, with \( \angle FBA = 20° \). #### To Find: - We need to determine the measure of angle \( \angle CDE \). This problem involves understanding the relationships between radii, chords, and angles subtended by these chords at the center and the circumference of the circle. Utilize properties such as the sum of angles in a circle and the relationship between central and inscribed angles to find the solution.
Transcribed Image Text:### Geometry Problem: Finding the Measure of Angle CDE #### Problem Statement: 5. Find the measure of angle \( \angle CDE \). #### Diagram Description: - The given diagram is a circle with center at point \( B \). - The circle is intersected by several lines. - Points \( C \), \( D \), and \( E \) are marked on the circumference such that \( C \), \( D \), and \( E \) form part of a closed path. - Point \( A \) also lies on the circumference, with line segment \( FA \) making a 20° angle with line segment \( BA \). - There is a right angle (90°) shown at point \( B \). In the diagram: - \( BE \) extends from the center \( B \) to the circumference at point \( E \). - \( BD \) extends from the center \( B \) to the circumference at point \( D \). - \( BA \) also extends from the center \( B \) to the circumference, with \( \angle FBA = 20° \). #### To Find: - We need to determine the measure of angle \( \angle CDE \). This problem involves understanding the relationships between radii, chords, and angles subtended by these chords at the center and the circumference of the circle. Utilize properties such as the sum of angles in a circle and the relationship between central and inscribed angles to find the solution.
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