## Do you know your SAT polygons?

A quick little formula that will make your life a lot easier in case you come across an SAT problem that asks about polygons is the following:

Total degree measures of a polygon: 180(n – 2), where n = # of sides of the polygon

Say, you have to find the total degree measure of an octagon (that’s the shape of a stop sign). But no need to stop here! We can just plug in ‘8’ for n and we get:

180(8 – 2) = 180(6) = 1080

Another helpful formula to know is the degree measure of any one side of a congruent polygon. A congruent polygon has equal sides, and therefore equal angles. All you have to do is to take the original formula and divide by ‘n’. This makes sense because you are taking the total degree measure and finding out the measure for any one side. So that’s why we divide the total degrees by the number of sides:

[180(n – 2)]/n

Returning to n = 8, let’s assume the octagon is congruent. What is the measure of any of its sides?

180(6) = 1080/n = 1080/8 = 160

Now you’ve learned two useful formulas dealing with polygons!

Degree measure of sides in a congruent polygon:

[(n – 2)180]/n