Each interior angle of a regular polygon has a measure of 162. How many sides does the polygon have ?

#2) If each interior angle has a measure of 162º, then each exterior angle has a measure of 180-162=18º.

How many angles are there ? The sum of the measures of the exterior angles of a convex polygon of

*n*sides is 360º. 360/18=20 angles and therefore 20 sides.check:There are 20 angles of 162º each for a total of 162*20=3240º

To find the sum of all the interior angles of a regular polygon you use the formula (n-2)180 where n=# of sides.

(20-2)(180)=18(180)=3240º