The proof of the
Explanation of Solution
According to the Polygon Exterior Angles Sum Theorem, the sum of the measures of exterior angles of convex polygon, having one angle at each vertex is 360.
According to the Polygon Interior Angles Sum Theorem, the sum of the measures of interior angles of an n-sided convex polygon is
Every angle in the interior of the polygon forms a linear pair with its exterior angle.
The sum of measures of linear pair is 180.
Therefore,
Sum of the measures of exterior angles = Sum of the measures of linear pairs − Sum of the measures of interior angles.
Thus, the sum of the measures of exterior angles of a convex polygon is 360.
Chapter 6 Solutions
Geometry, Student Edition
Additional Math Textbook Solutions
Essentials of Statistics, Books a la Carte Edition (5th Edition)
College Algebra
College Algebra (7th Edition)
Thinking Mathematically (7th Edition)
University Calculus: Early Transcendentals (3rd Edition)
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning