6-1 The Polygon Angle-Sum Theorems
Objectives
To find the sum of the measures of the interior angles of a polygon
To find the sum of the measures of the exterior angles of a polygon
Dynamic Activity
Polygon Angle-Sum Theorem
Lesson Vocabulary
- equilateral polygon
- equiangular polygon
- regular polygon
The Solve It is related to a formula for the sum of the interior angle measures of a polygon. (In this textbook, a polygon is convex unless otherwise stated.)
Essential Understanding The sum of the interior angle measures of a polygon depends on the number of sides the polygon has.
By dividing a polygon with n sides into
Take note Theorem 6-1: Polygon Angle-Sum Theorem
The sum of the measures of the interior angles of an n-gon is
Problem 1 Finding a Polygon Angle Sum
What is the sum of the interior angle measures of a heptagon?
Think
How many sides does a heptagon have?
A heptagon has 7 sides.
The sum of the interior angle measures of a heptagon is 900.
✓ Got It?
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- What is the sum of the interior angle measures of a 17-gon?
- Reasoning The sum of the interior angle measures of a polygon is 1980. How can you find the number of sides in the polygon?
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs