four angles of a pentagon have measures of 85*, 90*, 95*, and 110*.?
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!
134261
Its a scalene traingle. Here x works out to be 10.\n2x+x+40+4X+35= 180. x is nearly 10. Since all the lengths are different its a scalene triangle. The indivudual lengths work out to be 20,50,75.
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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°
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The average was (90-50)/20 = 2 lower than it should have been; thus 76.\n\nSide length = sqrt(625) = 25, so 4*25 = 100 inches.\n\n2/18 * 360 = 40.
441947
pentagon DUH! lol sry (Hexagon is SIX!)im in geometry rite now so yea
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One of the most simple requirements for tiling: if a polygon tiles a plane, then in each of polygon vertexes on the plane, the sum of adjacent angles should equal 360 degrees (one of the angles may be a side of another polygon, making up 180 degrees). \n\nFor example, imagine or draw a "house-shaped" pentagon, that is a square with a right-angled triangle on top (right angle pointing up). It has two angles of 90 degrees at the bottom, two 135 degree angles where "walls" and "roof" meet, and a 90 degree angle at the top ("roof" tip). You can tile them side-by-side and then tile the same pentagons on top, flipped upside down. At the "tip of the roof", you will see that two 135 degree angles and one 90 degree angle meet. 135+135+90=360. If it would not be the case, there would be a crack in the tiling.\n\nHowever, some polygons have such angle values that it is impossible to make a sum of angles equal to 360 or 180 degrees. For example, consider regular pentagons. They have angles of 108 degrees. However you add up 108 degree angles, you cannot make up 360 or 180.
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Take the average between the side of an inscribed square\nand that of an inscribed hexagon. With a hexagon you\nget an isosceles triangle with base as a side and a 60\ndegree angle at the apex, leaving 120 degrees to be split\nbetween the equal pair which are then also each 60 degrees.\nSo you have an equilateral triangle whose base is equal\nto the radius of the circle and of course the base is a side\nwhich has a length of 1. \n  Now inscribe a square. There are now 4 isosceles\ntriangles with a 90 degree angle at the apex and a pair\nof 45's at the base. Draw an altitude from the apex, \nperpendicular to the base, thus bisecting the 90 at\nthe apex making another 90, 45, 45 triangle whose\nside is 1/2 the side of that of the square. The hypotenuse\nis a radius of the circle so the side of the last mentioned\ntriangle is 1/2^2 (.707). This makes the side of the\nsquare 1.414. So averaging 1 and 1.414 you get 1.207.\n Using trig we find the real answer to be 1.1755.\nSo the percentage of error is 2.67 percent from 1.207.\nI wouldn't win an engineering prize with that kind of\naccuracy, but I think I could build a pretty good\ncatapult.
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+90° rotation (ie 90° anticlockwise)\nA = (0, -5) → (-5, 0)\nB = (1, 9) → (-9, 1)\nC = (8, 9) → (-9, 8)\nD = (-3, -1) → (1, -3)\n\n-90° rotation (ie 90° clockwise)\n\nA = (0, -5) → (5, 0)\nB = (1, 9) → (9, -1)\nC = (8, 9) → (9, -8)\nD = (-3, -1) → (-1, 3)
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A pair of angles are supplementary if their respective measures sum to 180 degrees.\n\nYou would subtract an angle less than 180 to get it's supplement.
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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
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the base angles are equal therfore each is (180-25deg17')/2\nso each is 155deg43'/2   which is 77deg51.5' which as a decimal is  is 77.8583degrees\n\nNOW circular measure is The measure of an angle in radians.\nThere are 2*Pi radians in 360deg therefore\n1deg = PI/180 rads\ntherefore\n77.8583degrees= 77.8583 times Pi/180 rads\n\ntake Pi as 3.142 and a calculator gives 1.359 rads
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By Thinkquest:  90°.  When one looks at a right prism, one can count all the right angles formed, and it will always be more than any non-right angles formed.
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Complement angles equal 90 degrees, therefore\n\n\n90 = larger (x) + smaller (x-25)\n\n90 = x + x - 25\n\n90 = 2x - 25  (add 25 to both sides)\n\n90 + 25 = 2x   or 115 = 2x\n\ndivide both sides by 2\n\nx = 57.5 degrees (larger angle)\n\nsmaller angle = larger angle - 25\n\nsmaller = 57.5 - 25 = 32.5 degrees\n\nAnswer 32.5 degrees
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a hectagon is 100 sides, a pentagon is 5. there is no specific formula for calculating the area of a pentagon but you can divide it into different shapes like triangles and trapaziums and work out the area of those shapes and add them together.
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For any polygon, you take the number of sides, subtract 2, and then multiply by 180.\n\nEx.  Triangle  (3-2)180 = 180\n     Quadrilateral (4-2)180 = 360\n     Pentagon (5-2)180 = 540\n\nAny polygon with n sides  (n-2)*180\n\n\nthen, if it is a regular polygon, (all sides and angles congruent), then divide that number by the number of sides.\n\n( (n-2)*180 ) /n
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You would just do 180-56 to equal 124 degrees\n\nsupplementary angles add up together to equal 180 degres or a straight line
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a pentagon, or a regular pentagon, depending on if all the sides & angles are equal or not. hope that helped.