Sides from the Exterior
Part of the Polygons & Quadrilaterals section of Coddy's Geometry journey. Lesson 14 of 61.
The exterior angle gives the number of sides of a regular polygon quickly. Each exterior angle is 360 / n, so if every exterior angle is 45°, then 360 / n = 45.
Multiply both sides by n to bring it out of the bottom: 360 = 45 × n. Divide by 45: n = 8. The polygon is a regular octagon.
From an interior angle, take it from 180° first. A regular polygon with 135° in each corner has exterior angles of 45°, so it has 8 sides, with no equation to expand.
Challenge
Each exterior angle of a regular polygon is 24°. The board shows the exterior angle formula as an equation in n. Solve it for n, then press Check.
Try it yourself
Solve for n
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Polygons & Quadrilaterals
1Polygons
Polygons and DiagonalsAngles of a QuadrilateralAngles in Any PolygonPolygon Angles with xHow Many Sides?Recap: Polygon Angles4Parallelograms
ParallelogramsNeighbouring AnglesOpposite AnglesParallelograms with xA Diagonal InsideRecap: Parallelograms2Regular Polygons
Regular PolygonsFrom an Angle to the SidesInside a Regular PolygonRecap: Regular Polygons5Rectangles, Rhombi, Squares
RectanglesThe Diagonal of a RectangleRhombus AnglesSquaresRecap: Special Parallelograms3Exterior Angles
Exterior AnglesExterior Angles Make 360°Regular Exterior AnglesSides from the ExteriorRecap: Exterior Angles6Trapezoids and Kites
TrapezoidsIsosceles TrapezoidsTrapezoids with xKitesRecap: Trapezoids and Kites