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Find the value of x. 2x - 6 6

Find the value of x. 2x - 6 6

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 presents a diagram of a triangle with an exterior angle. The task is to find the value of \( x \). ### Diagram Details: - The triangle is shown with two angles marked inside and one exterior angle. - One interior angle of the triangle is labeled as \( 2x - 6 \). - Another interior angle is unlabeled. - The exterior angle, adjacent to the side of the triangle with the angle of \( 2x - 6 \), is labeled as \( 6 \). ### Explanation: The problem involves understanding the relationship between the interior angles of a triangle and its exterior angle. According to the exterior angle theorem, the exterior angle is equal to the sum of the two non-adjacent interior angles. **Objective:** Find the value of \( x \) that satisfies the equation derived from this relationship. This exercise helps in understanding angle relationships within a triangle and applying algebraic methods to solve for \( x \).
Transcribed Image Text:The image presents a diagram of a triangle with an exterior angle. The task is to find the value of \( x \). ### Diagram Details: - The triangle is shown with two angles marked inside and one exterior angle. - One interior angle of the triangle is labeled as \( 2x - 6 \). - Another interior angle is unlabeled. - The exterior angle, adjacent to the side of the triangle with the angle of \( 2x - 6 \), is labeled as \( 6 \). ### Explanation: The problem involves understanding the relationship between the interior angles of a triangle and its exterior angle. According to the exterior angle theorem, the exterior angle is equal to the sum of the two non-adjacent interior angles. **Objective:** Find the value of \( x \) that satisfies the equation derived from this relationship. This exercise helps in understanding angle relationships within a triangle and applying algebraic methods to solve for \( x \).
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