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Geometry for School and Home
Activity 3.8
Assignment 3.9
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Assignment 4.13
The Sum of the Measures of the Angles of a Polygon
Objective
Develop a theorem for the sum of the measures of the angles of a convex polygon.
Apply the formula: S=180(n-2) to calculate the sum of the angle measures in polygons.
About Geometry Worksheet Assignment 4.13:
Assignment 4.13 is an introduction to the theorem for the sum of the measures of the angles in polygons.
Prerequisite Skills: Classify polygons (Assignment 3.3). Identify the sum of the measures of the angles of a triangle (Assignment 4.8). Evaluate algebraic expressions.
Theorems: The diagonals drawn from one vertex of a polygon divide the polygon into triangles.
The number of triangles determined by all diagonals drawn from one vertex of a convex polygon is two less than the number of sides in the polygon.
In a polygon with n sides, the number of triangles is n-2.
The sum of the measures of the angles of any convex polygon is 180 times the number of triangles formed by diagonals drawn from one vertex.
The formula for the sum of the measures of the angles of any convex polygon is S = 180 (n-2).