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
![**Finding the Measure of Angle CEB**
Given Diagram:
- Circle with points labeled A, B, C, and D on the circumference, and point E inside the circle.
- Line segments AB and CD intersect at point E.
- Angle ∠BAE is given as 45°.
- Angle ∠BCD is given as 109°.
To find: \( m∠CEB \)
\[
m∠CEB = \_\_\_\_\_\_
\]
Explanation:
1. Identify the intersecting chords: In this circle, AB and CD are the intersecting chords.
2. Understand that when two chords intersect inside a circle, the measure of the angle formed is half the sum of the measures of the intercepted arcs.
Given angles are crucial to the solution, and identifying the polygons formed can guide the steps for the solution process.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc32fdead-cf8a-44ab-a7f8-9f10e201d4c1%2F02162f43-de53-4cfe-add8-3e57917c737b%2F8p66zjn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Measure of Angle CEB**
Given Diagram:
- Circle with points labeled A, B, C, and D on the circumference, and point E inside the circle.
- Line segments AB and CD intersect at point E.
- Angle ∠BAE is given as 45°.
- Angle ∠BCD is given as 109°.
To find: \( m∠CEB \)
\[
m∠CEB = \_\_\_\_\_\_
\]
Explanation:
1. Identify the intersecting chords: In this circle, AB and CD are the intersecting chords.
2. Understand that when two chords intersect inside a circle, the measure of the angle formed is half the sum of the measures of the intercepted arcs.
Given angles are crucial to the solution, and identifying the polygons formed can guide the steps for the solution process.
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