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Algebra Find the values of m, 14. 45 mo %23

Algebra Find the values of m, 14. 45 mo %23

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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**Algebra: Find the values of \( m \) and \( n \).** **Problem 14** **Diagram Explanation:** The diagram shows two triangles sharing a common side. - The left triangle is a right triangle with a 45-degree angle indicated. - The angle adjacent to the right angle is labeled as 45 degrees, making this an isosceles right triangle. - The larger triangle has the following: - An angle of 60 degrees near the center. - One angle labeled as \( n^\circ \) and another labeled as \( m^\circ \). - The bottom right angle links the two triangles. **Equations and Relationships:** 1. **Main Triangle:** - Sum of angles in a triangle: \( 60^\circ + m^\circ + n^\circ = 180^\circ \) 2. **Sub-triangle (Right Triangle):** - Right angle = 90 degrees - Other angles = 45 degrees each; base angles of an isosceles right triangle 3. **Geometric Properties:** - The line with two identical markings indicates equal length sides. - The line with one identical marking at the bottom is marked for reference but has no additional data given.
Transcribed Image Text:**Algebra: Find the values of \( m \) and \( n \).** **Problem 14** **Diagram Explanation:** The diagram shows two triangles sharing a common side. - The left triangle is a right triangle with a 45-degree angle indicated. - The angle adjacent to the right angle is labeled as 45 degrees, making this an isosceles right triangle. - The larger triangle has the following: - An angle of 60 degrees near the center. - One angle labeled as \( n^\circ \) and another labeled as \( m^\circ \). - The bottom right angle links the two triangles. **Equations and Relationships:** 1. **Main Triangle:** - Sum of angles in a triangle: \( 60^\circ + m^\circ + n^\circ = 180^\circ \) 2. **Sub-triangle (Right Triangle):** - Right angle = 90 degrees - Other angles = 45 degrees each; base angles of an isosceles right triangle 3. **Geometric Properties:** - The line with two identical markings indicates equal length sides. - The line with one identical marking at the bottom is marked for reference but has no additional data given.
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