In this Grade 7 lesson from Big Ideas Math Advanced 2, students learn how to find the sum of interior angle measures of a polygon using the formula S = (n − 2) × 180°, and discover that the sum of exterior angle measures of any convex polygon is always 360°. Students also distinguish between convex and concave polygons and apply the interior angle sum formula to find missing angle measures in polygons such as pentagons, hexagons, and heptagons. The lesson builds from hands-on exploration activities to formal key ideas and real-life applications involving regular and irregular polygons.
Section 1
Polygon Definition and Classification
A polygon is a closed plane figure formed by three or more line segments that meet only at their endpoints. Polygons are classified as convex if all line segments connecting any two vertices lie inside the polygon, or concave if at least one line segment connecting two vertices lies outside the polygon.
Section 2
Polygon Interior Angle Sum Formula
The sum of interior angles of any polygon with sides is given by:
This formula is derived by dividing any polygon into triangles from one vertex.
Section 3
Exterior Angle Sum Property
The sum of all exterior angles of any polygon is always , regardless of the number of sides.
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Section 1
Polygon Definition and Classification
A polygon is a closed plane figure formed by three or more line segments that meet only at their endpoints. Polygons are classified as convex if all line segments connecting any two vertices lie inside the polygon, or concave if at least one line segment connecting two vertices lies outside the polygon.
Section 2
Polygon Interior Angle Sum Formula
The sum of interior angles of any polygon with sides is given by:
This formula is derived by dividing any polygon into triangles from one vertex.
Section 3
Exterior Angle Sum Property
The sum of all exterior angles of any polygon is always , regardless of the number of sides.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter