Could anyone tell me the answers to either or both of these questions?\n\n1. What is the sum of the interior angles of a regular octagon?\n\n2. What is the sum of the exterior angles of a regular octagon?
213835
1. 1080 degrees\n\n2. 1800 degrees
412607
I am not sure if I understand your question correctly, or else your question is not complete.\nFor example, a usual question of this sort is to find the maximum area of a rectangle for a given perimeter, the classical fence problem, as follows:\n\nYou are given a specific length of fence L to make en enclosure of maximum area.  What would be the dimensions of the rectangle.\n\nHere we take the length of one side as x, then the other side will be (L-2x)/2.  The area is thus A(x)=x(L-2x)/2.\n\nTo obtain the value of x for a maximum area, we differentiate A with respect to x, \ndA(x)/dx = d(Lx/2-x^2)=L/2-2x\nfor maximum area, dA(x)/dx=0, so we equate\nL/2-2x=0\nand solving for x gives x=L/4.\n\nThat means that the maximum area rectangle for a given perimeter is a square!\n\nHope that helps with your project.\nPost if you need other information, but please post details, especially how far you are with your project, so we can help you better.
276301
Your statement is incorrect.  It reads:\n\n"In the image below, there are right angles. How would I prove that they're right angles without a protractor in any triangle?"\n\nActually, it should read:\n\n"In the image below, there are some angles."\n\nAnything else is pure conjecture.  (That means a guess.)\n\nIf you would like us to say something about those angles, you need to tell us how the figure was constructed.  After you tell us that, and ask your question more clearly, your answer will be obtained in short order.\n\nedit...\n\nYou have added some text in your extra text file that doesn't help at all:\n\n"I know that these green points are right angles..."\n\nSo you think a point can also be an angle.  It will be a long time before you get someone (who knows and understands geometry) to agree with that.\n\nIf you start over and explain what you want to know, in correct terms, you may have a chance at getting an answer.
99914
im a geo student, but i havent done proofs for a long time sorry. ok\n2. false, because squares are parallelograms with 4 congruent sides and 4 right angles, while kites have 2 pairs of congruent sides and only 1 pair of congruent angles that are NOT right angles\n3. false, because a rhombus is a parallelogram with 4 congruent sides, while a kite is any thing BUT a parallelogram. enuff said\n4. false, because kites are quadrilaterals with only two pairs of congruent sides, while the quadrilateral mentioned has 3 congruent sides\n5. false, for example- do trapezoids have 4 congruent sides, and 4 right angles, and is a parallelogram (characteristic of squares)? i think NOT\n6. read above- trapezoids are not parallelograms.
562964
(a) You can flip a hexagon horizontally or vertically across a line, and you'll end up with the same hexagon.\n(b) Assuming that point is in the middle, every 60° you'll have the same hexagon.\n(c) Rotate it 30° from the center and the hexagon will appear rotated.\n(d) 120° is a multiple of 60°.\n\nThe answer is C.
516743
Hi. Don't you hate these? OK you have an unknown angle. Call it a. You have a complement, c, which is 90-a. c=3a-10. Any help?
391193
1. All angles are equal\n2. All angles are less than 180° \n3. Size of each angle = (180 - 360/n)° where n = number of sides
598839
|sin(z)|^2 + |cos(z)|^2\n\nWhere |f(z)|^2 is understood to mean f(z)*~f(z), where ~f(z) is the complex congugate of f(z): ~f(x + iy) = f(x - iy)\n\nWriting the real and imaginary parts of the arguments explicitly, we have:\n\n= |sin(x+iy)|^2 + |cos(x+iy)|^2\n\nUsing the sum of angles formulas:\n\n= |(sin(x)cos(iy) + cos(x)sin(iy)|^2 + \n  |(cos(x)cos(iy) - sin(x)sin(iy)|^2\n\nExpanding in terms of complex congugates:\n\n= ((sin(x)cos(iy) + cos(x)sin(iy))*(sin(x)cos(-iy) + cos(x)sin(-iy)) +\n  ((cos(x)cos(iy) - sin(x)sin(iy))*(cos(x)cos(-iy) - sin(x)sin(-iy))\n\nNoting that cos(-x) = cos(x) and sin(-x) = -sin(x):\n\n= ((sin(x)cos(iy) + cos(x)sin(iy))*(sin(x)cos(iy) - cos(x)sin(iy)) +\n  ((cos(x)cos(iy) - sin(x)sin(iy))*(cos(x)cos(iy) + sin(x)sin(iy))\n\n\nMultiplying this out (both terms are the product of a sum and difference of two terms, which yield the difference of squares):\n\n= (sin(x)cos(iy))^2 - (cos(x)sin(iy))^2 + (cos(x)cos(iy))^2 - (sin(x)sin(iy))^2\n\nFactoring:\n\n= ((sin(x))^2 + (cos(x))^2)*cos(iy) - ((sin(x))^2 + (cos(x))^2)*sin(iy)\n\nbut ((sin(x))^2 + (cos(x))^2) = 1, so\n\n= (cos(iy))^2 - (sin(iy))^2\n\nFrom Euler's formula (exp(ix) = cos(x) + i*sin(x)), we can show that:\n\ncos(iy) = (exp(-y) + exp(y))/2 = cosh(y)\nand\nsin(iy) = (exp(-y) - exp(y))/(2*i) = i*sinh(y)\n\nSubstituting these identities in for cos(iy) and sin(iy), we have:\n\n= (cosh(y))^2 - (i*sinh(y))^2 \n\n= (cosh(y))^2 + (sinh(y))^2\nQED
39850
how do you din the height of a trapezoid if one of the non parallel sides is straight, and the other is slanted. Which makes the two parallel sides different lengths? Also, how would you find the width of a trapezoid in this situation?\n\nIf the length of the shorter parallel side is A and the length of the longer parallel side is B and the length of the straight side is C and the length of the slanted side is D then:\n\nthe height is:\nh = C (the length of the straight side.\n\nThe width depends on where you measure the width.\n\nI am imagining that your trapezoid looks like this:\n.__\n/__|
266665
I'm afraid that with the given information, this would be impossible to determine. The only thing one could conclude from this information is that this polygon has an even number of sides. \n\nIt could be a square with sides of 3cm each\nIt could be a hexagon with sides of 2cm each\nIt could be an octagon with sides of 1.5cm each\nIt could be a decagon with sides of 1.2cm each\nIt could be a 12-gon with sides of 1cm each\n\nThe list is infinite unless you are given more specific information, such as the length of each side or the angles within the shape.
324495
number of sides, congurency?, size of angles, distinguishing characteristics
320537
There is no work to show, rather theorems to justify the solutions.\n\nInscribed angles of a circle that subtend a diameter are 90 degrees. This is a corollary of a theorem which states that inscribed angles are 1/2 the measure of a sector angle which subtends the same arc. In the diameter case the sector angle is 180 degrees, thus the inscribed angles are 90.\n\nThe quadrilateral that contains angle Z has it's vertices on the circumference and is cyclic. A cyclic quadrilateral has the property that opposite angles are supplimentary (add  up to 180) thus angle Z = 180 - 148 = 32 degrees.\n\nI am not sure how you would show work toher than proving the theorems.\n\nHope it helps
216964
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!
141257
The dimesnions of the rectangle are 14 feet by 34 feet.\n\nYou know that the perimeter is 96 feet and that each long side is 20 feet more than the short sides.\n\nAs there are 2 long sides the total length of both these sides must be 40 feet more than the total length of the 2 short sides (20 x 2 = 40).\n\nIf all the sides were the same length as the short sides then the rectangle would have a perimeter of 56 feet (we know it's 96 feet to start with and that the additional length on the two long sides is 40 feet and 96 - 40 = 56).\n\nEach side would therefore be 14 feet long since 56 divided by 4 = 14.\n\nNow that we know the length of the short sides all we need to do is add 20 to get the length of the long sides, 14 + 20 = 34.\n\nTo check it you can add 14 + 14 (the two short sides) + 34 + 34 (the two long sides) = 96.\n\nI hope that makes sense, it's 1:25AM here and I'm getting tired.
323051
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!
536612
Hi babygurl, \nAll you have to remember is that the exterior angle measures ALWAYS add up to 360 degrees, no matter how many there are.  So just divide 360 by the number of sides to get the measure of any one exterior angle (assuming it's a regular polygon so all the angles are the same).\n 360/4=90.
333284
Question 20906\nSubmitted on 5/28/2002\n\nFind the area of a nonagon inscribed in a circle of radius 24cm.\n\nSolution 20906\n\nThe nonagon can be divided into nine congruent isosceles triangles. \nThe lengths of the sides are 24 cm and the vertex angle is 360/9 = 40.\nThe base of one triangle is\nB = 2 * 24 * sin (20)\nThe height of the triangle is\nh = 24 * cos (20)\nSo the area of one triangle is\nA = (1/2) * 2 * 24 * sin (20) * 24 * cos (20)\nA = 24^2 sin(20) cos(20)\nAnd the area of the nonagon is\n9 * 24^2 sin (20) cos (20)\n= 1666.1\n\n\nSubstitute in your 1 meter for the 24 centimeters and you'll get your answer.  I believe the answer should come out to somewhere around 3.353 m^2