The sum of the interior angles of a polygon with sides is
.Example 2
Whatis the sum of the interioranglesof a nonagon?To find the sum of the interioranglesin a nonagon,use the expressionabove.Rememberthat a nonagon
has nine sides,so will be equalto nine.
So, the sum of the interioranglesin a nonagonis.InteriorAnglesin Quadrilaterals
A quadrilateralis a polygonwith four sides,so you can find out the sum of the interioranglesof a convex
quadrilateralusingour formula.
Example 3
Whatis the sum of the interioranglesin a quadrilateral?Use the expressionto find the valueof the interioranglesin a quadrilateral.Sincea quadrilateralhas four
sides,the valueof will be 4.
So, the sum of the measuresof the interioranglesin a quadrilateralis.This will be true for any type of convexquadrilateral.You’ll exploremoretypeslater in this chapter, but they
will all haveinterioranglesthat sum to. Similarly, you can divideany quadrilateralinto two triangles.
This will be helpfulfor manydifferenttypesof proofsas well.
LessonSummary
In this lesson,we exploredinterioranglesin polygons.Specifically, we havelearned:
- How to identifythe interioranglesof convexpolygons.
- How to find the sumsof interioranglesin convexpolygons.
- How to identifythe specialpropertiesof interioranglesin convexquadrilaterals.
Understandingthe anglesformedon the insideof polygonsis one of the first stepsto understandingshapes
and figures.Thinkabouthow you can applywhatyou havelearnedto differentproblemsas you approach