a definition for angles in a triangle?
86738
The angles all add up to 180 degrees.\n\nIf you know the lengths of all the sides you can use the "Law of Tangents" to find all the angles.  This is advanced geometry and Trigonometry, so rather than type, I am including a link to a pretty good explanation.\n\nhttp://answers.google.com/answers/threadview?id=38131
1170465
the larger the angle, the longer the opposite side. the smallest angle in a triangle has the shortest opposite side; the largest angle has the longest opposite side
87753
Just add up the lengths of the three sides. Works for any triangle - wether it's equilateral, isosceles or obtuse.
963860
where is the right angle in the triangle.  Between the right and bottom, between the bottom and left?  Without knowing this, we can't tell you the answer.\n\nBUT\nin a right triangle\nhypotenuse squared = side 1 squared + side 2 squared
987754
Actually the only way it would be possible is if you use Elliptic or Riemannian geometry, and would require a manifold.  A representation of such a construct would be similar to drawing a 4 dimensional shape in 3 or even 2 dimensions.\n\nEuclidian geometry doesn't allow triangles with a sum of all angles to be greater than 180 degrees.
726903
since the sum of two  angles is equal to the one angle it  imlies the third angle is 90 degree since \nbecause:\nLet the angles be a,b,c now a+b=c therefore a+b+c=180 now a+b=c therefore 2c=180 this implies c=90 degrees. therefore it is a right triangle hence the measure of the third side according to pythagoras therom is square root of the sum of the squares of both sides
675746
by the number of sides and angles
811153
Hi, \n\nThe answer lies in the pythagorean theorem. \n\nFor any right (one of the angles is 90 degrees) triangle with sides a,b and c where c is the side opposite the 90 degree angle:\n\na^2 + b^2 = c^2\n\nso for your first excercise:\n\na = 4\nb = 4 Sqrt(3)\nc = ?\n\na^2 + b^2 = c^2\n4^2 + {4 Sqrt(3)}^2 = c^2\n16 + 4^2 * 3 = c^2\n16 + 16 * 3 = c^2\n64 = c^2 \nc = +- 8 (since we're dealing with a triangle, -8 doesn't make sense, so just ignore it.)\n\nc = 8. \n\nFollow that same pattern, and you should be all set. \n\nHope that helps, \nMatt
710344
C - 3 possible answers\n\nIn any given right triangles with the two other angles being a and b,\n\nsin a = cos b AND sin b = cos a,\n\n\nas such, the first and fourth combination will give one answer, the other two will either give square trigonometric values of each angle i.e. sin^2 a and cos^2 a  OR sin^2 b and cos^2 b.\n\nThe only condition that will not satisfy this is when the angle is 45 degrees, which means a = b and contradicting the given statement of a being less than b.\n\nThus the answer is C.
367687
an angle that is inside a circle or any other figure
217384
you mean if you have two angles?  For angles x,y,z of a triangle:\n\nx + y + z = 180\n\nI'll let you go from there...
892546
1) a triangle and an ext angle by given.\n2) 1+2+3=180 by the sum of interiors of a triangle\n3) 3+4= 180 by linear pair postulate (or theorem, i forgot)\n4) 1+2+3=4+3 by Transitive property\n5) 1+2=4 by Subtraction property.
611646
Simply bisect the obtuse triangle once and only once through point at which the A side and B side intersect through the middle of C. \n\nSince a triangle, by defintion, has 3 angles that equal 180 degrees, the smallest angles would be, using whole numbers for clarity, 178deg, 1deg and 1 deg. Bisecting the 178deg angle makes two 89deg angles, which is under the definition of an acute angle. \n\nSince an acute angle is defined as an angle less than 90deg, and a triangle is defined as having 3 angles with a sum of 180deg, we know that the 180deg can not be just one angle (180deg, when bisected, creates 2 right angles) and still be a triangle. Therefore, we know that for any triangle ABC with an obtuse angle at AB, bisecting the angle once, and only once, through AB to the midpoint of C will create two right triangles with angles of 90deg, 90deg - angle#1deg, and 90deg - angle#2deg.
356323
Absurd... A triangle cannot have more than 1 obtuse angle, since the sum of all angles of a triangle is 180 degrees.
1043313
It's too cumbersome to rewrite it all here, but check out http://www.euclideanspace.com/maths/algebra/vectors/angleBetween/index.htm\n\nThat's 2D, but the formula is the same for 3D.
965531
ALL triangles are ALWAYS 180 degrees.\nIf a triangle is "right", that means that one angle is 90 degrees.....meaning that the other two angles have to also equel to 90 degrees.....\nComplimentary means two angles equeling 90 degrees.....therefore, both of the acute angles are compimentary because they have no choice in the matter
800930
No - similar triangles have the same angles (so a triangle with a 90 degree angle can't be similar to a triangle without a 90 degree angle).\n\nEdit - responding to Ona below:\nI don't know where you got your definition of 'acute triangle' from, but acute triangle means every angle is strictly less than 90 degrees. If one of its angles is 90 degrees, it is simply a right triangle, not 'acute and right'. (Google for acute triangle and see if you can find a definition that matches yours..)