Regular Polygon Angle Measures
Regular polygon angle measures is a Grade 7 geometry concept in Big Ideas Math Advanced 2, Chapter 3: Angles and Triangles, providing formulas for each interior and exterior angle. Each interior angle of a regular n-gon equals (n minus 2) times 180 degrees divided by n, and each exterior angle equals 360 degrees divided by n. For example, each interior angle of a regular hexagon is 720 divided by 6 equals 120 degrees.
Key Concepts
For a regular polygon with $n$ sides: Each interior angle = $\frac{(n 2) \times 180°}{n}$ Each exterior angle = $\frac{360°}{n}$.
Common Questions
What is the formula for each interior angle of a regular polygon?
Each interior angle equals (n minus 2) times 180 degrees divided by n, where n is the number of sides. For a regular pentagon, this is (5 minus 2) times 180 divided by 5 equals 108 degrees.
What is the formula for each exterior angle of a regular polygon?
Each exterior angle equals 360 degrees divided by n, where n is the number of sides. For a regular octagon, each exterior angle is 360 divided by 8 equals 45 degrees.
Why does the interior angle formula use (n-2)?
The interior angle sum formula is (n minus 2) times 180 degrees because any polygon can be divided into (n minus 2) triangles, each contributing 180 degrees. Dividing by n gives each individual angle.
What textbook covers regular polygon angle measures in Grade 7?
Big Ideas Math Advanced 2, Chapter 3: Angles and Triangles covers interior and exterior angle formulas for regular polygons.