The sum of the measures of the interior angles of a convex polygon is 1260 deg. Find the no. of sides of the?
822232
Use the formula (n-2)*180 =1260 to solve this problem. Start by dividing both sides by 180 to get:(n-2)=7. This means that n=9
930936
Use the fact that the sum of the angles of a triangle add up to 180 degrees. Let A, B, C be the angles of the triangle. The m<A + m<B + m<C =180. If you know m<A and m<B, you can find m<C.\n\nWhen I write m<A, I mean the measure of angle A, not m is less than A.
851122
An easy way to do this is to remember that the *exterior angles* of a polygon always add up to 360°.\n\nSo one exterior angle of a regular hexagon will be 360°/6 = 60°\n\nThe interior angle is always the supplement (180° - 60°), so it will be 120°.  Since there are 6 angles that means 720°.\n\nAnother general formula for the sum of the interior angles is:\n(n-2) * 180°, where n is the number of sides.  In your case you have 6 sides, so 4 * 180° = 720°.\n\nA final way to figure the sum of the interior angles is to build a table.  Each time you add 180°.\n\nTriangle = 3 sides = 180°\nSquare = 4 sides = 360°\nPentagon = 5 sides = 540°\nHexagon = 6 sides = 720°\n...\n\nAny way you figure the answer, you should get 720°.
703752
simply subtract 7 from both sides. This leave you with\n\nx<_3
794240
Let n = number of sides = 5\n\nSum of the interior angles = (n - 2) * 180° = 540°\n\nThis comes from the fact that a triangle has angles adding to 180°, a square has angles adding to 360°, a pentagon has angles adding to 540°, etc.  Each time you add a side, you add another 180 degrees.\n\nHowever there are no 1 sides or 2 sided figures, so you have to subtract 2 from the sides, before multiplying.\n\nThe general formula for an n-sided polygon is:\n(n - 2) * 180°
633697
a heptagon is also known as a septagon, and it has seven sides.  \n\nthe angle used to construct a regular heptagon is 128.57 degrees.\n\nhere is a picture of a heptagon.  if you print it and measure each inner angle with your protractor, it will prove the angle of the dangle.\n\nhow is this angle derived?\n\na = (n-2 ) X (360 / (n x 2))\n\nwill give you the inner-angle for any regular polygon with n sides.\n\ntriangle (3 sides)\n\n3-2 X 360/(3 x 2)\n1 X 360/6\n1 X 60\n60 degrees\n\nsquare (4 sides)\n\n4-2 X 360 / (4 X 2)\n2 X 360/8\n2 X 45\n90 degrees
644806
if the triangle is a regular triangle\n\na = (1/2)bh\n\na = (1/2)(6)(6 * sin60)\n\na = (1/2)(6)(3√3)\n\na = 9√3 = 15.588\n\n\nfor a regular polygon, \narea = (n*t^2) / (4*tan(π/n))\n\nwhere n = number of sides & t = length of side
158697
his saying the area not the other side.\na= bh/2\nu know that this parallelogram is a rectangle and if u put adiagonal angle abc is a right. so u'll just use the formula\n12*13 over 2\n=78 units.
63969
A hexagon has 6 sides.
46001
you need to be more specific...\nbut technicaly the perimeter is the sum of all the sides...
626304
An Angle sum of any polygon is (n-2)*180.\n\nOctagon has 8 sides - so it is (8-2)*180 = 1080 degrees\n\nThe proof of this is simple. Any polygon can be divided into (n-2) non overlapping triangles which share the same end points as the polygon (try it on paper its easier to understand).\nSince we already know that sum of angles of a triangle is 180 degrees. We get angle sum of any polygon as (n-2) * 180 degrees.\n\nFor example, a rectangle can be divided into two triangles (by drawing a line along the diagonal) - add up the angles of each triangle - 180 degrees each. Sum both these to get the angle sum of the rectangle. Which is 180 + 180 = 360.
897859
I find this an interesting question, and I suspect there are several possible methods for solving it.  However, I recommend we deal with it straightforwardly by solving for, say, the base length, height ... any 'variables' found within these polygons' area formulas.\n\nThe understanding here is that both polygons are regular polygons (the triangle is therefore equilateral, the hexagon has 6 equal-length sides, etc.).\n\nThe most creative solutions (and least mathematical) would probably involve cutting up one of the shapes and "re-gluing" it to form the other, thereby gaining some hint at the relationship between their perimeters.\n\nI normally prefer straight math, and would recall:\n\n A(triangle) = (1/2) base * height\n A(hexagon) = ([3sqrt(3)]/2) (side)^2\n\nBut let's "logic" our way through this one first.  Think of the hexagon as being composed of 6 equilateral triangles, each containing 1/6 of the overall area.  Because the original hexagon had an area in 1:1 ratio with the given triangle, we now can state:\n\n Area (SmallTriangle) = (1/6) (BigTriangle)\n\nRecalling a particular theorem concerning similar polygons ("The ratio of their areas will be the square of the ratio of their sides"), we can take this further:\n\n Ratio of BigTri:SmallTri Areas = 6:1\n\nSo,\n\n Ratio of BigTri:SmallTri Sides = sqrt(6):1\n\nPicture now how the small triangles would be "glued together" to form their parent hexagon.  Only the "outside side" would contribute to the hexagon's perimeter ... SIX such sides would be needed.  In short:\n\n Ratio of hexagon perimeter:BigTri perimeter = 6sqrt(6):1\n\nHope this (is correct and) helps!
1092713
triskaidecagon\n\nor a 13-sided polygon, haha.\n\nCheck the source for polygon names from 1-20 sides  :)
23529
that is one of the answers, if the length of one side is 5. Use the Phytagorous theorem.
24746
I think the sum of all internal angels of a polygon is given by (n-2)*180. So, for a 40 sided polygon, it should be (40-2)*180=38*180=6840 I guess.
917109
for a polygon with n sides, the sum of all interior angles would be 180*(n-2) degrees.\n\nSo a nonagon would be 180*(9-2) = 180*7 = 1260 degrees\nan 11-agon would be 180 * (11-2) = 1620 degrees
74297
(# sides - 2) * 180 = sum of all the interior angles\n\n[(# sides - 2) * 180]/(# sides) = each interior angle if they're all congruent