How Many Sides?

Part of the Polygons & Quadrilaterals section of Coddy's Geometry journey. Lesson 3 of 59.

The corners of a floor tile add up to 1080°. Each triangle inside gives 180°. Then $\frac{1080}{180} = 6$ , so the tile has 6 triangles inside. A polygon has 2 more sides than triangles. So the tile has 8 sides. As an equation:

$\left(n-2\right)\cdot 180 = 1080$

$n-2 = 6$

$n = 8$

The angle sum is always a whole number of 180s. So no polygon has angles that add up to 1000°.

Challenge

A polygon's angles add up to 1440°. How many sides does it have? Write your working. Finish with n = the number of sides.

Then press Check.

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All lessons in Polygons & Quadrilaterals

2Regular Polygons

Regular Polygons 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