Find the number of sides of a regular polygon whose interior angle measures 108 degrees. How do I do this?
453387
5. Here's how you do it:\n\n108x = 180(x-2)\n\n(the "x-2" comes from dividing the pentagon into triangles. All polygons follow the rule a = 180(s-2), where a is the sum of the interior angles, and s is the number of sides in the polygon.)\n\n108x = 180x - 360\n72x = 360\nx = 5
914112
It's usually called a quadrilateral, and the total of the internal angles of a convex quadrilateral is 360º.\n\nTo figure the sum of the internal angles of any convex polygon, the formula is (n-2)*180º, so a pentagon (five sides) has 540º, a hexagon (six sides) has 720º and so forth.
583148
Well, lets see if we can generate a pattern.\n\nA 3-sided polygon (aka a triangle) has no diagonals\nA 4-sided has 2\nA 5-sided has 5 (1-3, 2-4, 3-5, 4-1, 5-2)\nA 6-sided has 9 (1-3, 1-4, 1-5, 2-4, 2-5, 2-6, 3-5, 3-6, 4-6)...\nand so on.\n\nA polygon with n sides has n(n-3)/2 diagonals. The answer for 42 is left as an exercise for the reader ;)
814748
The obtuse angles of the trapezoids will be (in degrees) 90+invtan((57.35-29.27)/(2*27.54)), which is approximately 117 degrees.\n360 degrees minus the sum of two of these angles (126 degrees) is the interior angle of whatever regular polygon you are trying to make.\nThe interior angle of a regular hexagon is 120 degrees.\nThe interior angle of a regular heptagon (7-sided polygon) is approximately 128.57 degrees.\n\nTherefore, you could put 6 of these tables into a circular arrangement and have some extra space between the front edges of the tables, or you could put 7 of these tables into a circular arrangement (a better fit) and have a little bit of extra space between the back edges of the tables.\n\nIt would also look more interesting to have heptagonal arrangements of tables in the room.
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.
477711
The interior and exterior angle add up to 180 degrees; so far the smallest would be 180 - 110 = 70 degrees.  But since there are 5 angles in a pentagon, we have to first make sure that the unknown angle of the pentagon is not larger than 110 (making it's supplement, the exterior angle, smaller than 70 degrees.\n\nDraw a pentagon on your scratch paper (it doesn't have to be perfect) and pick one of the vertices (the "corners" where the sides meet).  If you draw a line from that vertex to all of the other vertices, you see that you've divided the pentagon into 3 triangles.  Since each triangle has 180 degrees, the whole pentagon has angles that add up to 3 x 180 or 540 degrees.  From the four angles you've been told (85 + 90 + 95 + 110 = 380) you can figure out that the fifth angle has to be 160 degrees (540 - 380 = 160).  So the exterior angle that matches up with that angle is 180 - 160 = 20 degrees and choice B. is correct!
1114001
c = 108 degrees\nyou can find this since A + B + c = 180\nA=B+C+72\nThensubstitute to get A + A + A + 72 = 180\n3A + 72 = 180\nA = 36 so then C= 108
29941
You can't have a polygon of that size.  A polygon is an object with three or more straight sides.  One property of a polygon is that no one side can be longer than all the other sides added together.  You listed 6 dimensions, implying a six sided polygon.  But since one side is much longer than the other five together, this is not a real object.\n\nTry taking a yardstick and five toothpicks and put them together to make a polygon shape.  It won't work.\n\nIncidentally, even if you gave realistic dimensions, that's not enough information.  Consider this 6-sided object:\n._\n/ .&#92;\n&#92;_/\nand this one:\n||\n||\n||\n\nEven if the sides were all the same length, they have different areas because the angles are different.
606410
The formula for finding the number of degrees that all of the sides of a polygon add up to is 180(n-2), with N being the number of sides.\n\nTriange has 3 sides. 3-2=1. *180=180.\n\n180-51-32=97.\n\nThe answer is 97 degrees.\n\nI hope you like my thorough answer that explains how I got the answer, so you can do it yourself, and I just didn't tell you the answer.\n\n\nHope this helps!\nNate
184797
find the angle between two sides.
186903
the measure of the interior angle for a polygon is =(n-2)*(180)/n\n\nso you put 150 = (n-2)*(180)/n\nyou get (5/6)n - n + 2 = 0\nn = 12\n\nyou have 12 sides
687079
An equilateral triangle is a regular polygon with three equilateral sides (sides measuring the same length) and three equiangular angles (angles that are the same measure) these being of 60 degrees.
942453
From symmetry, you have all the angles\n69 for two, and 180-69= 111 for the other two.\nUse the law of cosines: for triangle abc with opposing angles A,B,C we have the length of the 3rd side c for given a,b from:\n\nc = sqrt(a^2 +b^2 -2abcos(C))\n\nIn your case: a=4, b=6 and C = 69 so\n\nBD = sqrt(36+16-48(cos(69)) = 5.9\n\nFor C = 111 we have:\n\nAC = sqrt(36+16-48(cos(111))= 8.32
747405
15 inches\nThe side of a regular hexagon inscribed in a circle is the same as the radius of the circle. In fact, if you connect the center of the circle to each vertex of the hexagon (with a straight line segment), then you will have 6 equilateral triangles that all meet at the center of the circle.
607716
If the circles are all tangent to each other, then you can draw lines from center to center to center.  Thus, you'd have a triangle with sides 8, 12, and 10 (each side is formed by adding two radii).  So you can find the angles using the law of cosines:\n\nc^2 = a^2 + b^2 - 2abcos(c)\n8^2 = 12^2 + 10^2 - 2(12)(10)cos(c)\n64 = 144 + 100 - 240cos(c)\n240cos(c) = 180\ncos(c) = 3/4\nc ~ 41 deg\n\nAnd then just change up numbers to find the other angles:\n\nb^2 = a^2 + c^2 - 2accos(b)\n10^2 = 12^2 + 8^2 - 2(12)(8)cos(b)\n100 = 144 + 64 - 192cos(b)\n192cos(b) = 108\ncos(b) = 9/16\nb ~ 56 deg\n\na^2 = b^2 + c^2 - 2bccos(a)\n12^2 = 10^2 + 8^2 - 2(10)(8)cos(a)\n144 = 100 + 64 - 160cos(a)\n160cos(a) = 20\ncos(a) = 1/8\na ~ 83 deg\n\nAnd this checks out since 41 + 56 + 83 = 180.
666685
Assuming the box is square, one angle will be 90 degrees.\n\nA stop sign is a regular octogon (8 sides). So the total of the internal angles is (8-2)x180 = 1080\nDivide this by 8 to find the size of each angle (only works in a regular shape) 135.\n\nThe other two angles are both '180 degrees (a straight line) subtract 135 degrees' 180-135= 45 degrees.\n\nNext time, listen in class!
29433
Good question, but I think you meant pentagon.\n\nIf you had a regular pentagon with a side of 1, then the triangle formed any two adjacent sides of the pentagon, the third side equals Phi.\n\nTo check we can use the law of Sines.\n\nSin A / a = Sin B / b = Sin C / c\n\nEach interior angle of a regular polygon is found by this formula:\n\n180(n - 2) / n, when n = the number of sides the polygon has.\n\nSo, for a regular pentagon\n\n180(5 - 2) / 5\n180(3) / 5\n540 / 5\n108 degrees\n\nSince the triangle we formed is an isoscles one, the other 2 angles can be found out by subtracting 108 from 180 and dividing the result by 2.\n(180 - 108)/2 = 72/2 = 36 degrees\n\nSin 108 / Phi = Sin 36 / 1\n\nThe formula for Phi is:\n5 ^ .5 * .5 + .5\n\nArcSin(Sin 108 / (5 ^ .5 * .5 + .5)) = \n= ArcSin(0.9510565163 / 1.618033989) = \n= ArcSin(0.5877852523) = 36