Let X be the set of all even positive integers n such that the measure of the angle of some regular polygon is n degrees. Find the number of elements in X .

Step-by-step solution

Let number of sides of polygon be P . (P-2) 180^ P =n^ then P(180-n)=360 P= 360 180-n But n=2 k then P= 180 90-k Hence possible values of (90-k) are 1,2,3,4,5,6,9,10,12,15,18,20,30,36,45 and 60 16 such polygons are possible.