Sum of the interior, and or exterior angles of a regular octagon...?
471637
1. 1080 degrees\n\n2. 1800 degrees
733210
You basically have 2 options. Use a protractor and measure them (The internal angles total 180 degrees).\n\nThe other option is using the trig functions (Sin, cos and tan), however you must have some info on the triangle eg. length of sides to apply any of these.
63969
A hexagon has 6 sides.
457243
octagon\nholy water\nsilence
18728
Again I assume you are talking about vector addition.  In this case you use trig the angle and magnitude given to find the x and y components for each vector.  Then just add all of the x componets together and all of the y components together to get the sum.  Then you can use the pathagorean theorem and arctan to find the magnitude and direction of the resultant vector.
858717
oblique, obilisque shape
945908
Hi Dear Ruth ; \n\n{ as you know Sum ( angles of trapezoid) = 360\nif ' a ' & ' b ' & ' c ' & ' d ' are angles of trapezoid so \na + b + c + d = 360 } ....\n\n▪ Step 1 \na = 6x - 4   , b = 5x + 1 , c = 4x  , d = 3x + 3\nas , a + b + c + d = 360 so ;\n6x - 4 + 5x + 1 + 4x + 3x + 3 = 360\n[ 6x + 5x + 4x + 3x  ] + [ -4 + 1 + 3 ] = 360\n18x + 0 = 360 \nx = 360 / 14\nx = 20 \n\n▪ Step 2\nas x = 20 \na = 6x - 4  ; 6(20) - 4 = 116 \nb = 5x + 1 ; 5(20) + 1 = 101\nc = 4x ; 4(20) = 80 \nd = 3x + 3 ; 3(20) + 3 = 63\nso we have ;\na = 116 ; b = 101 , c = 80 , d = 63 \n\nGood Luck dear ♣
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
898306
Unfortunately, the people above have misused geometry.\n\nThe way that you'd solve this in a geometry class would involved quite a bit of trigonometry. Here's a way to solve it without using as much. (I worked it out both ways and both methods give the same result. I also checked the result.)\n\nI'm assuming that your octagon is regular.\n\nDraw a regular octagon. Call the length of each side a.\n\nNow use vertical and horizontal lines to draw gridlines on the octogon. This divides the octagon into four triangles, four rectangles, and a square in the middle.\n\nThe square has area a^2..\n\nThe triangles are 45-45-90 triangles having hypotenuse a. This means that both sides are a / square root of 2. This means that each triangle has area:\n\n1/2 * (a / sqr(2)) * (a / sqr(2)) = a^2 / 4.\n\nThe rectangles have one side that is a side of the octagon (a) and one side that is a leg of the triangle (a / sqr(2)).\n\nThis means that the rectangles have area:\n\na * (a / sqr(2)) = a^2 / sqr(2).\n\nThe octagon's area is equal to the sum of the areas of its regions:\n\n4 triangles + 4 rectangles + 1 square\n\n4*(a^2 / 4) + 4*(a^2 / sqr(2)) + a^2 = \n\na^2 + 2sqr(2)*a^2 + a^2 = \n\na^2 (2 + 2sqr(2)) = 64.\n\nSolve for a, and you get approximately 3.6407 feet.\n\nThat is to say, an octagon having a side length of 3.6407 feet has the same area as a square having a side length of 8 feet.\n\nThis seems contradictory until you realize that an regular octagon isn't made up of just squares and triangles. If they were, then the "diagonal" sides would be longer than the "horizontal" and "vertical" sides.
695430
There's not enough information to answer the question. We need to know at least one angle as well as the length of two 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.
967111
Square and regular hexagon together \n\nEach decagon is surrounded on each alternate side by a square and a hexagon\n\nAlternately instead of the regular hexagon you could put 6 equilateral triangles tesselated into a regular hexagon or a combination of hexagons and equilateral triangles.
706305
R^2=A^2+B^2 -2(A*B)cos(180-acute angle)
932014
The measure of the exterior angle of a triangle must be greater than the measure of either non-adjacent interior angle.\n\nThis is because the measures of the exterior angle and its adjacent interior angle must add up to 180 since they are a linear pair.  But the measures of the two non-adjacent interior angles must also add with the adjacent one to get 180 since the measures of the 3 angles of a triangle add up to 180.\n\nSo the exterior angle's measure equals the sum of the two non-adjacent interior angles, and therefore must be bigger than either one of them.\n\nGood luck, hope that helps.
643430
7 gon is known as heptagon.\n\nremember this : one exterior angle of polygon=\n                               360/(sides of polygon)\n          thus for heptagon: one exterior angle=360/7\n                                               =51.428 deg\ntotal sum of exterior angles=  360 degrees
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.
289202
If you know the side length of the octagon (regular octagon)\nand let call it (a) then the area will be :\nArea=2 a2 cot PI/8 \n    =2(1+square root of 2)*a2\n    it is about 4.82843 a2\n\nExample if the side length of an octagon is 100 ft the are \nwill be :\nArea = 2(1+ 1.41421)* 100*100\n     = 48284.271  ft2.