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Geometry · JSS 1

Exterior angles of a polygon

Find the number of sides of a regular polygon from one angle.

  • Sum of exterior angles = 360°
  • Each exterior angle of a regular polygon = 360°n

What the letters mean

n
the number of sides

Worked example

Each exterior angle of a regular polygon is 24°. How many sides has it?

  1. Step 1: Rearrange

    n = 360°24° = 15

Final answer: 15 sides

Interior angle + exterior angle = 180° at every corner.

See it

Play with this picture from the Plane Shapes lesson.

Rectangle · a quadrilateral

Sides
4
Right angles
4
Parallel pairs
2
Lines of symmetry
2
Regular?
No
Angle sum
360°
(4 − 2) × 180° = 360°

Tick marks show equal sides; arrows show parallel sides.