| An equilateral polygon is a polygon with all sides congruent. | An equiangular polygon is a polygon with all angles congruent. | A regular polygon is a polygon that is both equilateral and equiangular. |
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Take note: Corollary to the Polygon Angle-Sum Theorem
The measure of each interior angle of a regular n-gon is
You will prove the Corollary to the Polygon Angle-Sum Theorem in Exercise 43.
Problem 2 Using the Polygon Angle-Sum Theorem
Biology The common housefly, Musca domestica, has eyes that consist of approximately 4000 facets. Each facet is a regular hexagon. What is the measure of each interior angle in one hexagonal facet?
Think
How does the word regular help you answer the question?
The word regular tells you that each angle has the same measure.
The measure of each interior angle in one hexagonal facet is 120.
✓ Got It?
- What is the measure of each interior angle in a regular nonagon?
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