As you can tell, thereare two possibleexterioranglesfor any givenvertexon a polygon.In the figureabove
we only showedone set of exteriorangles;the otherset wouldbe formedby extendingeachside in the
opposite(clockwise)direction.However, it doesn’tmatterwhichexterioranglesyou use becauseon each
vertextheir measurementwill be the same.Let’s look closelyat one vertex,and drawboth of the exterior
anglesthat are possible.
As you can see, the two exterioranglesat the samevertexare verticalangles.Sinceverticalanglesare
congruent,the two exterioranglespossiblearounda singlevertexare congruent.
Additionally, becausethe exterioranglewill be a linearpair with its adjacentinteriorangle,it will alwaysbe
supplementaryto that interiorangle.As a reminder, supplementaryangleshavea sum of.
Example 1
Whatis the measureof the exteriorangle in the diagrambelow?