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B C 60° 50° 30° 20⁰ E A

B C 60° 50° 30° 20⁰ E 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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Question
This diagram depicts a geometric figure composed of triangles with four labeled points: \( A \), \( B \), \( C \), \( E \), and \( F \). The outer triangle is labeled \( \triangle ABC \), and within this triangle, lines \( BF \) and \( CE \) intersect at point \( x \). The known angles in the diagram are as follows: - \(\angle CBA = 60^\circ\) - \(\angle ABE = 20^\circ\) - \(\angle BCF = 50^\circ\) - \(\angle BCA = 30^\circ\) The angles of the lines forming the inner section of the triangle are not labeled except for angle \( \angle CEF = x \), which is the angle to be determined. This diagram mainly focuses on evaluating the internal angles with respect to the known degrees and how these relate to solve for \( x \). The figure requires application of geometric principles to derive the value of \( x \) through angle relationships and possibly angle sum properties within triangles.
Transcribed Image Text:This diagram depicts a geometric figure composed of triangles with four labeled points: \( A \), \( B \), \( C \), \( E \), and \( F \). The outer triangle is labeled \( \triangle ABC \), and within this triangle, lines \( BF \) and \( CE \) intersect at point \( x \). The known angles in the diagram are as follows: - \(\angle CBA = 60^\circ\) - \(\angle ABE = 20^\circ\) - \(\angle BCF = 50^\circ\) - \(\angle BCA = 30^\circ\) The angles of the lines forming the inner section of the triangle are not labeled except for angle \( \angle CEF = x \), which is the angle to be determined. This diagram mainly focuses on evaluating the internal angles with respect to the known degrees and how these relate to solve for \( x \). The figure requires application of geometric principles to derive the value of \( x \) through angle relationships and possibly angle sum properties within triangles.
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