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Given the B-sided figure below with exterior angle measures as shown, what is the value of X? 75° 68% A B C D 15 x=148 x=125" x=55* x= 105⁰ 32⁰ 28% 201

Given the B-sided figure below with exterior angle measures as shown, what is the value of X? 75° 68% A B C D 15 x=148 x=125" x=55* x= 105⁰ 32⁰ 28% 201

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:** Given the 8-sided figure below with exterior angle measures as shown, what is the value of \( x \)? **Diagram:** In the diagram, an 8-sided irregular polygon is presented with the following exterior angles labeled (clockwise from the top as seen in the provided figure): - \( 68^\circ \) - \( 75^\circ \) - \( x \) - \( 67^\circ \) - \( 20^\circ \) - \( 28^\circ \) - \( 32^\circ \) - \( 15^\circ \) **Answer Choices:** A) \( x = 148^\circ \) B) \( x = 125^\circ \) C) \( x = 55^\circ \) D) \( x = 105^\circ \) **Solution:** To determine the value of \( x \), recall that the sum of all exterior angles of any polygon is always \( 360^\circ \). Sum of given exterior angles + \( x \) = \( 360^\circ \) So, \( 68 + 75 + x + 67 + 20 + 28 + 32 + 15 = 360 \) Calculating the sum of the known exterior angles: \( 68 + 75 + 67 + 20 + 28 + 32 + 15 = 305 \) Now, solve for \( x \): \( 305 + x = 360 \) \( x = 360 - 305 \) \( x = 55 \) **Correct Answer:** C) \( x = 55^\circ \)
Transcribed Image Text:**Problem Statement:** Given the 8-sided figure below with exterior angle measures as shown, what is the value of \( x \)? **Diagram:** In the diagram, an 8-sided irregular polygon is presented with the following exterior angles labeled (clockwise from the top as seen in the provided figure): - \( 68^\circ \) - \( 75^\circ \) - \( x \) - \( 67^\circ \) - \( 20^\circ \) - \( 28^\circ \) - \( 32^\circ \) - \( 15^\circ \) **Answer Choices:** A) \( x = 148^\circ \) B) \( x = 125^\circ \) C) \( x = 55^\circ \) D) \( x = 105^\circ \) **Solution:** To determine the value of \( x \), recall that the sum of all exterior angles of any polygon is always \( 360^\circ \). Sum of given exterior angles + \( x \) = \( 360^\circ \) So, \( 68 + 75 + x + 67 + 20 + 28 + 32 + 15 = 360 \) Calculating the sum of the known exterior angles: \( 68 + 75 + 67 + 20 + 28 + 32 + 15 = 305 \) Now, solve for \( x \): \( 305 + x = 360 \) \( x = 360 - 305 \) \( x = 55 \) **Correct Answer:** C) \( x = 55^\circ \)
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