equationwherewe set all of the exterioranglesshown(including ) summedand equalto
. Usingsubtraction,we can find the valueof.
The measureof the missingexteriorangleis.We can verifythat our answeris reasonableby inspectingthe diagramand checkingwhetherthe anglein
questionis acute,right,or obtuse.Sincethe angleshouldbe obtuse, is a reasonableanswer(assuming
the diagramis accurate).
LessonSummary
In this lesson,we exploredexterioranglesin polygons.Specifically, we havelearned:
- How to identifythe exterioranglesof convexpolygons.
- How to find the sumsof exterioranglesin convexpolygons.
We havealso shownone exampleof how knowingthe sum of the exterioranglescan help you find the
measureof particularexteriorangles.
LessonExercises
For exercises1-3, find the measureof eachof the labeledanglesin the diagram.