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Based on the 102° measures B provided in the diagram, D determine the measure of the angle e.

Based on the 102° measures B provided in the diagram, D determine the measure of the angle e.

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 Statement: Based on the measures provided in the diagram, determine the measure of the angle \( \theta \). (Note: You may assume that point A is the center of the circle and that DC is a diameter.) (Figure may not be drawn to scale.) ### Diagram Explanation: - The figure is a circle with points B, C, and D on its circumference and point A at its center. - Line segment \( DC \) is the diameter of the circle. - The measure of angle \( \angle BDC \) is \( 102^\circ \). - Angle \( \theta \) is located at vertex D, between segments \( BD \) and \( DC \). ### Choices: - \( 78^\circ \) - \( 39^\circ \) - \( 51^\circ \) - \( 48^\circ \) ### Explanation: Using the fact that \( DC \) is a diameter, note that angle \( \angle BDC = 102^\circ \) is an angle subtended by the diameter of the circle. Therefore, \( \theta \) is the interior angle that needs to be calculated based on the given conditions.
Transcribed Image Text:### Problem Statement: Based on the measures provided in the diagram, determine the measure of the angle \( \theta \). (Note: You may assume that point A is the center of the circle and that DC is a diameter.) (Figure may not be drawn to scale.) ### Diagram Explanation: - The figure is a circle with points B, C, and D on its circumference and point A at its center. - Line segment \( DC \) is the diameter of the circle. - The measure of angle \( \angle BDC \) is \( 102^\circ \). - Angle \( \theta \) is located at vertex D, between segments \( BD \) and \( DC \). ### Choices: - \( 78^\circ \) - \( 39^\circ \) - \( 51^\circ \) - \( 48^\circ \) ### Explanation: Using the fact that \( DC \) is a diameter, note that angle \( \angle BDC = 102^\circ \) is an angle subtended by the diameter of the circle. Therefore, \( \theta \) is the interior angle that needs to be calculated based on the given conditions.
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