<p>I need help solving this problem</p>
<p>I do not understand it at all :O</p>
<p>Thanks in advance</p>
<p>The edge of the paper and the polygon form a quadrilateral. The interior angles of the quadrilateral include x, y, and two of the interior angles of the regular polygon (which are all equal—let’s call this angle z). Because the interior angles of a quadrilateral sum to 360 degrees, we know that x+y+2z=360. Since we are told that x+y=80, we can substitute this into the former equation (i.e. x+y+2z=360 becomes 80+2z=360). Solving for z, we get 2z=280 and z=140. Since the sum of the interior angles of a polygon is equal to 180(n-2), we know that 140n = 180(n-2). This becomes 140n = 180n - 360 -> 40n = 360 -> n = 9. Thus, the polygon has nine sides.</p>
<p>ahhhh thanks 
I got it now</p>
<p>Hi!</p>
<p>Can you explain to me why the equation is 140n=180(n-2)?
I understand that 180(n-2) would give me the number of sides, however i do not understand the 140n.</p>
<p>Each angle is 140 degrees and the number of angles (or number of sides) is n, so 140n would be the sum of the interior angles. The formula for the sum of interior angles is 180(n-2), so set them equal to each other and solve.</p>
<p>180(n-2) is an expression for the sum of the interior angles of the polygon (where n is the number of sides); since the sum of the interior angles of a regular polygon is the number of interior angles times the measure of each angles, we get 140n as an equivalent expression for the sum of the interior angles.</p>
<p>For clarification </p>
<p>180(n - 2) is derived using triangles. Think about it: a triangle (3 sides) has a total of 180 degrees of interior angles. 180(3 - 2) = 180</p>
<p>A quadrilateral can be divided up into two triangles. 180(4 - 2) = 360. It’s just the same as saying 180 * 2 = 360 because it can be divided into two triangles. </p>
<p>Because the number of sides and angles in a given convex regular polygon are equal, you can just divide the sum of the interior angles by n to get the individual interior angle size.</p>
<p>Thank everyone I get it now!</p>
<p>Without the 140n=180(n-2) thing.</p>
<p>Exterior angle 180-140=40,
the sum of exterior angles = 360, therefore the number of angles = 360/40=9.</p>