How Many Sides?

Part of the Polygons & Quadrilaterals section of Coddy's Geometry journey. Lesson 5 of 61.

The angle sum formula works backwards too. If a polygon's angles add up to 1440°, write the formula as an equation in n, the number of sides: (n - 2) × 180 = 1440.

Divide both sides by 180: n - 2 = 8. Add 2: n = 10. The polygon has 10 sides. Check it: 10 − 2 = 8 triangles, and 8 × 180 = 1440.

The angle sum of a polygon is always a whole number of 180s, because n − 2 counts whole triangles. A total like 1000° belongs to no polygon at all.

Challenge

A polygon's angles add up to 1260°. The board shows the angle sum formula as an equation in n. Solve it for n, the number of sides, then press Check.

Try it yourself

(n - 2) * 180 = 1260

Solve for n

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Polygons & Quadrilaterals

2Regular Polygons

Regular Polygons From an Angle to the Sides Inside a Regular Polygon Recap: Regular Polygons

5Rectangles, Rhombi, Squares

Rectangles The Diagonal of a Rectangle Rhombus Angles Squares Recap: Special Parallelograms

8Area of Parallelograms

Area of a Rectangle A Side from the Area Slide the Top Area of a Parallelogram Recap: Parallelogram Area

11Polygon Chases

Parallel Sides in a Pentagon Marks, Not Looks Pentagon with x Regular Shapes Together Recap: Polygon Chases