<p>ok so there is this one problem that I really don't get. (i searched everywhere, even on khan and cc but no luck)
its section 2 problem number 17.
it says
In the figure above, a shaded polygon which has equal sides and equal angles is partially covered with a sheet of blank of blank paper. If x+y=80, how many sides does the polygon have.
(A)Ten
(B)Nine
(C)Eight
(D)Seven
(E)Six</p>
<p>I thought that since it says sides then the #of angles is the same as the #of sides, i can plug in the sides. Say if there were 10 sides then to find the total sum of the inner angles i can uses the (#of angles-2)*180 formula. but it seems to not work</p>
<p>The shaded region is a quadrilateral. The remaining 2 angles will add up to 280 (360-80). Since we are told, the polygon is a regular polygon, each angle of the polygon is 140 (280/2).</p>
<p>The polygon that has 140 degrees for each vertex is a 9-sided polygon [(9-7)*180/9 = 140]. The answer’s is B.</p>
<p>but are we subtracting from 360 because we are assuming that x+ some degree=180 and y+some degree= 180 therefore x+y+some degree+ some degree=360?</p>
<p>We are subtracting 80 from 360 because the exposed shape is a quadrilateral. This means that all the angles add up to 360. Since the sum of two angles are given ( x + y) and they add up to 80 (the exact angle of x and y are unimportant), this means that the other two angles in the shaded quadrilateral add up to 280 (360-80 = 280). Since the problem says whatever shape this is (the rest is covered up), all the angles should be equal (do note that angles x and y are formed by the paper and are not the angles of the sides), so:</p>
<p>If you know that the sum of the exterior angles of any regular polygon is 360, then this problem is a little easier. Each exterior angle here is 180 - 140 = 40, which means that there are nine exterior angles and nine sides. Pretty tough problem any way you do it.</p>