Noticethat the hexagonaboveis dividedinto four triangles.
Sinceeachtrianglehas internalanglesthat sum to , you can find out the sum of the interiorangles
in the hexagon.The measureof eachanglein the hexagonis a sum of anglesfromthe triangles.Since
noneof the trianglesoverlap,we can obtainthe TOTAL measureof interioranglesin the hexagonby summing
all of the triangles'interiorangles.Or, multiplythe numberof trianglesby :
The sum of the interioranglesin the hexagonis.
Example 1
Whatis the sum of the interioranglesin the polygonbelow?The shapein the diagramis an octagon.Drawtriangleson the interiorusingthe sameprocess.The octagoncan be dividedinto six triangles.So, the sum of the internalangleswill be equalto the sum
of the anglesin the six triangles.
So, the sum of the interioranglesis.Whatyou may havenoticedfrom theseexamplesis that for any polygon,the numberof trianglesyou can
drawwill be two less than the numberof sides(or the numberof vertices).So, you can createan expression
for the sum of the interioranglesof any polygonusing for the numberof sideson the polygon.