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< 20 Find the measure of 21. A 21= B 50° 1 C degrees D

< 20 Find the measure of 21. A 21= B 50° 1 C degrees D

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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### Problem Find the measure of ∠1. ### Diagram Description 1. The diagram shows a circle with points labeled A, B, C, and D on the circumference. 2. Line segments form a quadrilateral inside the circle with the following points: - A chord from A to D. - A chord from B to C that intersects AD. 3. The given angle, ∠BCD, measures 50°. 4. Angle ∠1 is located at point B, inside the circle, separated from the given angle by the intersection of the chords. ### Question - What is the measure of ∠1? ### Solution Method Use the theorem for angles formed between two chords intersecting inside a circle. The measure of an angle formed by two intersecting chords is half the sum of the measures of the arcs intercepted by the angle and its vertical angle. ∠1 = 1/2(Arc AC + Arc BD) (The diagram appears simplified here; any additional information would be required for complete calculation.)
Transcribed Image Text:### Problem Find the measure of ∠1. ### Diagram Description 1. The diagram shows a circle with points labeled A, B, C, and D on the circumference. 2. Line segments form a quadrilateral inside the circle with the following points: - A chord from A to D. - A chord from B to C that intersects AD. 3. The given angle, ∠BCD, measures 50°. 4. Angle ∠1 is located at point B, inside the circle, separated from the given angle by the intersection of the chords. ### Question - What is the measure of ∠1? ### Solution Method Use the theorem for angles formed between two chords intersecting inside a circle. The measure of an angle formed by two intersecting chords is half the sum of the measures of the arcs intercepted by the angle and its vertical angle. ∠1 = 1/2(Arc AC + Arc BD) (The diagram appears simplified here; any additional information would be required for complete calculation.)
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