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4. If mLFAE = 65°, following: (Round to the nearest tenths, if necessary.) A. mLAGC= mLAFD=35°,mAB= 60°, and FA and GC are tangent to the circle, find the 650 B. mLABD = D E 60° 35 B C F

4. If mLFAE = 65°, following: (Round to the nearest tenths, if necessary.) A. mLAGC= mLAFD=35°,mAB= 60°, and FA and GC are tangent to the circle, find the 650 B. mLABD = D E 60° 35 B C F

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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On this educational exercise, students are asked to solve geometrical problems using a diagram of a circle with intersecting lines and tangents. **Problem Statement:** Given: - m∠FAE = 65° - m∠AFD = 35° - m∠AB = 60° - FA and GC are tangent to the circle Find the following (round to the nearest tenths if necessary): A. m∠ACG B. m∠ABD **Diagram Description:** The diagram features a circle with a few intersecting lines and segments: - Points \(A\), \(B\), \(C\), \(D\), \(E\), \(F\), and \(G\) are labeled. - \(FA\) and \(GC\) are tangent to the circle at points \(A\) and \(C\) respectively. - Line segments include \(FA\), \(AF\), \(FD\), \(AB\), \(BE\), and \(EG\). - Angles provided in the problem are shown as: - \(∠FAE = 65°\), which is an angle formed by the tangent \(FA\) and the intersecting segment \(AE\). - \(∠AFD = 35°\), which is an internal angle in the triangle \(AFD\). - \(∠AB = 60°\), which is marked along segment \(AB\). **Tasks:** 1. Students need to calculate the measure of angle \(∠ACG\). 2. Students need to find the measure of angle \(∠ABD\). When solving the tasks, students should employ concepts of circle geometry, use tangent properties, and apply the given angle measures effectively.
Transcribed Image Text:On this educational exercise, students are asked to solve geometrical problems using a diagram of a circle with intersecting lines and tangents. **Problem Statement:** Given: - m∠FAE = 65° - m∠AFD = 35° - m∠AB = 60° - FA and GC are tangent to the circle Find the following (round to the nearest tenths if necessary): A. m∠ACG B. m∠ABD **Diagram Description:** The diagram features a circle with a few intersecting lines and segments: - Points \(A\), \(B\), \(C\), \(D\), \(E\), \(F\), and \(G\) are labeled. - \(FA\) and \(GC\) are tangent to the circle at points \(A\) and \(C\) respectively. - Line segments include \(FA\), \(AF\), \(FD\), \(AB\), \(BE\), and \(EG\). - Angles provided in the problem are shown as: - \(∠FAE = 65°\), which is an angle formed by the tangent \(FA\) and the intersecting segment \(AE\). - \(∠AFD = 35°\), which is an internal angle in the triangle \(AFD\). - \(∠AB = 60°\), which is marked along segment \(AB\). **Tasks:** 1. Students need to calculate the measure of angle \(∠ACG\). 2. Students need to find the measure of angle \(∠ABD\). When solving the tasks, students should employ concepts of circle geometry, use tangent properties, and apply the given angle measures effectively.
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