Polygon Interior Angle Sum Formula
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 3: Angles and Triangles) learn the Polygon Interior Angle Sum Formula: S = (n - 2) x 180 degrees, where n is the number of sides. This formula works for any polygon by dividing it into (n - 2) triangles from one vertex.
Key Concepts
The sum of interior angles of any polygon with $n$ sides is given by: $$S = (n 2) \times 180°$$.
This formula is derived by dividing any polygon into $(n 2)$ triangles from one vertex.
Common Questions
What is the polygon interior angle sum formula in 7th grade?
The sum of interior angles of a polygon with n sides is S = (n-2) x 180 degrees. For a pentagon (n=5): S = (5-2) x 180 = 540 degrees.
How do you use the polygon angle sum formula to find a missing angle?
Calculate the total angle sum using S = (n-2) x 180. Add all known angles and subtract from S to find the missing angle.
Why does the polygon formula use (n - 2)?
Any polygon can be divided into (n-2) triangles from one vertex. Since each triangle has 180 degrees, total = (n-2) x 180 degrees.
What chapter in Big Ideas Math Advanced 2 covers the polygon interior angle sum?
Chapter 3: Angles and Triangles in Big Ideas Math Advanced 2 (Grade 7) covers the Polygon Interior Angle Sum Formula.
What is the interior angle sum for a hexagon?
A hexagon has 6 sides: S = (6-2) x 180 = 4 x 180 = 720 degrees.