Exterior Angle Topic Index | Geometry Index | Regents Exam Prep Center
 An exterior angle of a polygon is an angle that forms a linear pair with one of the angles of the polygon.
 Two exterior angles can be formed at each vertex of a polygon.  The exterior angle is formed by one side of the polygon and the extension of the adjacent side.  For the hexagon shown at the left, <1 and <2 are exterior angles for that vertex.  Be careful, as <3 is NOT an exterior angle.
 Note:  While it is possible to draw TWO (equal) exterior angles at each vertex of a polygon, the sum of the exterior angles formula uses only ONE exterior angle at each vertex.

 Formula: Sum exterior angles of any polygon = 360° (using one exterior angle at a vertex)

Finding the sum of the exterior angles of a polygon is simple.  No matter what type of polygon you have, the sum of the exterior angles is ALWAYS equal to 360°.

If you are working with a regular polygon, you can determine the size of EACH exterior angle by simply dividing the sum, 360, by the number of angles.   Remember, the formula below will ONLY work in a regular polygon.

 Formula:  Each exterior angle (regular polygon) =

 Examples

1.

Find the sum of the exterior angles of:
 a) a pentagon Answer:  3600 b) a decagon Answer:  3600 c) a 15 sided polygon Answer:  3600 d) a 7 sided polygon Answer:  3600

 2. Find the measure of each exterior angle of a regular hexagon. A hexagon has 6 sides, so  n = 6 Substitute in the formula.
 3. The measure of each exterior angle of a regular polygon is 45°.  How many sides does the polygon have ? Set the formula equal to 450. Cross multiply and solve for n.

 Topic Index | Geometry Index | Regents Exam Prep Center Created by Michael Murray