If two angles are congruent and supplementary, then each is a(n) __________angle.?
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A right angle.  \n\nSupplementary means the angles add up to 180˚, and congruent means they are the same size.  So for two angles to be both congruent and supplementary, they both need to be exactly half of 180˚.  Half of 180˚ is 90˚, so they are right angles.
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The first thing is to understand the difference between similar and congruent (identical).  Two triangles are similar if their shapes are similar, but their sizes may be different.  An equilateral triangle is similar to another equilateral triangle, but one could have sides of length 1 and the other sides of length 2.  These are *similar*.  But for them to be congruent both their angles and their sides would all have to be the same.\n\nLike you said, if two triangles had 2 angles the same (and therefore the 3rd angle must be known to be the same since they all add up to 180), then you've only proven them *similar*.  A side could be 3 units long, but if you doubled them all, you would still have a *similar* triangle, but it wouldn't be *congruent*.\n\nA concept commonly taught in high school mathematics is that of proving the "angle" and "side" theorems, which can be used to define two triangles as similar or congruent.\n\nIn each of these three-letter acronyms, A stands for equal angles, and S for equal sides. For example, ASA refers to an angle, side and angle that are all equal and adjacent, in that order.\n\nAAA - Angle-Angle-Angle. If two triangles share three common angles, they are *similar*. (Obviously, this means that the side lengths are locked in a common ratio, but can vary proportionally, making the triangles similar.) Additionally, since the interior angles of a triangle have a sum of 180°, having two triangles with only two common angles (sometimes known as AA) implies similarity as well. \n\nTwo triangles are *congruent* if their corresponding sides and angles are equal. Usually it is sufficient to establish the equality of three corresponding parts and use one of the following results to conclude the congruence of the two triangles:\n\nSAS (Side-Angle-Side): Two triangles are *congruent* if a pair of corresponding sides and the included angle are equal.\n\nSSS (Side-Side-Side): Two triangles are *congruent* if their corresponding sides are equal.\n\nASA (Angle-Side-Angle): Two triangles are *congruent* if a pair of corresponding angles and the included side are equal.\n\nWhile the AAS (Angle-Angle-Side) condition also guarantees *congruence*, SSA (Side-Side-Angle) does not, as there are often two dissimilar triangles with a pair of corresponding sides and a non-included angle equal. This is known as the ambiguous case. Of course, AAA (Angle-Angle-Angle) says nothing about the size of the two triangles and hence shows only *similarity* and not congruence.\n\nHowever, a special case of the SSA condition is the HL (Hypotenuse-Leg) condition. This is true because all right triangles (which this condition is used with) have a congruent angle (the right angle). If the hypotenuse and a certain leg of a triangle are congruent to the corresponding hypotenuse and leg of a different triangle, the two triangles are congruent.
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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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All you have to use is the fact that for any triangle, the measures of the three interior angles add to 180 degrees.  So if you have Triangles ABC and DEF, then you know:\nangleABC + angleBAC + angleBCA = 180 degrees, and\nangleDEF + angleEDF + angleEFD = 180 degrees.\n\nIf two angles are congruent, then they have the same measure in degrees.  So, if angleABC is congruent to angleDEF, and angleBAC is congruent to angleEDF, then:\nangleABC = angleDEF, and\nangleBAC = angleEDF.\n\nUsing substitution:\nangleABC + angleBAC + angleBCA = angleDEF + angleEDF + angleEFD\nangleDEF + angleBAC + angleBCA = angleDEF + angleEDF + angleEFD\nangleDEF + angleEDF + angleBCA = angleDEF + angleEDF + angleEFD.\n\nthen simplify by subtracting (angleDEF + angleEDF) from both sides:\n\nangleBCA = angleEFD.\n\ntherefore, the third angles are congruent.
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law of cosines : a^2 = b^2 + c^2 -2bc * cos(A)\nwhere a, b,c are side lengths and A is the angle oppisite side a.
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Let's call these angles A and B.  And let's call C the adjacent angle in the middle of these two angles.\n\nThen we will have:\n\nA + C = 180\nB + C = 180\n\nAs a result, A = B = 180 - C
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Adjacent sides of a rectangle...those are the sides that are at 90 degree angles of one another.  Sometimes, such as in squares, they are congruent.  They are not always congruent.  So, there's your answer, sometimes.
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1.  Opposite angles in a rhombus are congruent.\n2.  Adjacent angles in a rhombus are supplmentary.\n\n<LMK is half of one of the smaller angles, and <KJM is one of the larger angles.  So <LMJ will be 72, and since <LMJ and <KJM are supplementary, <KJM is 108.
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sin(2A)=sin(A+A)=sinAcosA + sinAcosA=2sinAcosA
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The previous answers are either wrong/incomplete/mischievious.\nFirstly there is nothing called parallel angles! You probably meant to ask what happens if the angles of two triangles are same. In that case there is no congruence/similarity between the two triangles.\nBut if two angles are equal betwen them, they are SIMILAR (same shape) and not congruent.\nIf in addition they have a side equal, they become congruent!
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Triangles XYZ and OYZ are congruent. We know this because the three sides are all congruent.\n\nXY congruent to XZ\nOY congruent to OZ\nYZ congruent to YZ (both triangles share this side)\n\nBecause the triangles are congruent, their corresponding angles must be congruent as well.
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supplementary angles = angles whose sum is 180 ° or pi radiants.\n\nSo, pi - 11/12.
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If the sides are parallel then these angles will be equal.
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The sum of the three angles of a triangle is 2 right angles.So ,if one of its angle is one right angle,then the sum of the other two angles would be one right angle,which makes it impossible for another angle to be a eight angle.
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a) "Suppose Triangle ABC and Triangle DEF are congruent."\nb) "Suppose there exists a line segment with at least two right bisectors."\nc) "Suppose there is an isosceles triangle for which the angles opposite two of its congruent sides are not congruent."\nd) "Suppose there is a line segment with at least two midpoints."\ne) "Suppose there are two intersecting lines such that opposite angles are not congruent."\nf) "Suppose AB is not equal to CD."
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Yeah where's angle 1 and 2.\nBut remember the angle opposite the longest side has the greastest measurement.
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Not a, since the congruent sides could be adjacent sides.\n\nNot b, because that would be a trapezoid.\n\nDefinitely c - there's a way to prove this using properties of parallel lines, interior angles, and triangles.\n\nMaybe d, since congruent diagonals means that your angles could be right angles, but it also could mean that you have an isosceles trapezoid.\n\nBisecting diagonals always means that your quadrilateral is a parallelogram.  Congruent diagonals can also yield a parallelogram, albeit a specialized one - a rectangle.  Now if you have diagonals that both bisect each other and are congruent, then you have a square.