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Click here to see ALL problems on PolygonsQuestion 488216: A 12-sided polygon will contain ?? right angles in the sum of its vertices. The answer is 10...but why? say thanks to you!! answer by Theo(11697) (Show Source): You have the right to put this systems on your website! the formula because that the sum of the internal angles of a polygon is same to (n-2)*180.the polygon has 12 sides, therefore the sum of the interior angles of the polygon is equal to (12-2)*180 = 10*180 = 1800 degrees.there are 12 angles in the polygon and it is presume to be a continual polygon (equal angles and equal sides), therefore each inner angles will be same to 1800 / 12 = 150 degrees.an interior angle and also a vertex walk together.each vertex contains an inner angle the is formed by the political parties connecting to that vertex.the source of the is together follows:a straight angle is an angle of 180 degrees.the formula stated over of (n-2) * 180 can be re-worded to say (n-2) * a straight angle.the formula relies on the truth that the sum of the angles of a triangle is equal to 180 degrees.accept that and also you can then have the formula indigenous that.look in ~ the snapshot below and also then read the comments listed below it.the sum of the angle in a triangle is equal to 180 degrees.each polygon can be separated into the same number of triangles as the sum of the sides of the triangle.each of this triangles has a vertex at the facility of the polygon.a rectangle has 4 sides and also can be split into 4 triangles.a hexagon has actually 6 sides and also can be separated into 6 triangle.the amount of the angle of the triangle in ~ the polygon is thus equal come the variety of sides * 180.if we want to get the sum of the inner angles of the polygon, we have to subtract the sum of the main angles of the polygon.the sum of the main angles that the polygon will always be same to 360 degrees due to the fact that the number of degrees in a circle is equal to 360 degrees.we therefore have to subtract 360 from the sum of the angles of the triangle that form the polygon to get the amount of the interior angles the the polygon.this method that ours formula becomes:n * 180 - 360.now, 360 is same to 2 * 180, for this reason our formula becomes:n * 180 - 2 * 180.if we element out the 180, climate we room left with (n-2) * 180.that"s exactly how the formula is derived.when you have actually a dodecagon, then it has 12 sides.the formula climate becomes:(12 - 2) * 180 which i do not care 10 * 180.here"s a attach that name the polygons.http://mathcentral.uregina.ca/qq/database/QQ.09.96/rosa1.htmlthe names room usually obtained from the greek names because that the variety of sides. 