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le below, UW is a diameter and UX is tangent at U. Suppose m UV=58°. Find the following. V (a) m Z VUW =0• (b) m Z VUX = 0•

le below, UW is a diameter and UX is tangent at U. Suppose m UV=58°. Find the following. V (a) m Z VUW =0• (b) m Z VUX = 0•

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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The image depicts a geometry problem involving a circle and a tangent line. Here is the transcription and explanation of the diagram: ### Problem Description: In the circle below, \( \overline{UW} \) is a diameter and \( \overline{UX} \) is tangent at \( U \). Suppose \( m \angle UV = 58^\circ \). Find the following: (a) \( m \angle VUW = \_\_^\circ \) (b) \( m \angle VUX = \_\_^\circ \) ### Diagram Explanation: - The circle has a diameter labeled \( \overline{UW} \). - A chord labeled \( \overline{UV} \) is shown within the circle. - A tangent line \( \overline{UX} \) is shown touching the circle at point \( U \). - Angle \( \angle UV \) is specified as \( 58^\circ \). ### Tasks: - Calculate the measure of angle \( \angle VUW \). - Calculate the measure of angle \( \angle VUX \). Note: The tangent-tangent angle property and other circle theorems might be useful in solving this problem.
Transcribed Image Text:The image depicts a geometry problem involving a circle and a tangent line. Here is the transcription and explanation of the diagram: ### Problem Description: In the circle below, \( \overline{UW} \) is a diameter and \( \overline{UX} \) is tangent at \( U \). Suppose \( m \angle UV = 58^\circ \). Find the following: (a) \( m \angle VUW = \_\_^\circ \) (b) \( m \angle VUX = \_\_^\circ \) ### Diagram Explanation: - The circle has a diameter labeled \( \overline{UW} \). - A chord labeled \( \overline{UV} \) is shown within the circle. - A tangent line \( \overline{UX} \) is shown touching the circle at point \( U \). - Angle \( \angle UV \) is specified as \( 58^\circ \). ### Tasks: - Calculate the measure of angle \( \angle VUW \). - Calculate the measure of angle \( \angle VUX \). Note: The tangent-tangent angle property and other circle theorems might be useful in solving this problem.
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