Triangle A B C has the property that ∠ A + ∠ B = ∠ C . Find the measure of ∠ C in degrees.
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Well, in an Euclidean geometry, this is true, but not in general
It's a type of triangle we called in class a 45-45-90 triangle, according to the measure of the angles. If one angle of a triangle is 90°, the other two must be 45° each.
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What about a 30-60-90?... Or other combinations?
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You are right....There can be all sorts of P & C for A+B=90.
I put 91 ans got it wrong. 91+44.5+44.5= 180. ????
Sorry guys I couldn't present my solution in the proper format.
Since A + B + C = 180; equation 1
and A + B = C; equation 2
Replace the value of C to equation 1.
Thus, A + B + A + B = 180;
2A + 2B = 180;
Therefore, 2 (A + B) = 180;
A+B = 90
From equation 2, C = 90.
Of all the solutions on this page......THIS one is how it's done.
Did you have to do it so long?
Congratulations- you just broke maths
A+B =C so, C+C=180 2C=180 C=90
The only case possible is, the triangle should be right angle triangle
Can you prove there are no other cases?
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Can you proove to disproove ?
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I'm assuming you mean "can you disprove it," in which case, can you disprove that unicorns exist?
According to a theorem in Geometry,
Angles A , B, and C sums up to a total of 180°
Hence, A + B + C = 180°
But since, A + B = C, and they'be ask for the measurement of angle C
It means that they must be pertaining to a complementary angle.
Since in a Complementary Angle
Angle A + Angle B = 90°
Thus, by means of common sense and appropriate knowledge of Geometry ,we say that
Angle A [Variable Value < 45° ] + Angle B [Variable Value <45°] = Angle C [Variable Value = or < 90°]
Sorry my friend v common sense does not prove anything from your solution.
Since A + B + C = 180; equation 1
and A + B = C; equation 2
Replace the value of C to equation 1.
Thus, A + B + A + B = 180;
2A + 2B = 180;
Therefore, 2 (A + B) = 180;
A+B = 90
From equation 2, C = 90.
A+B=C therefore C+C=180 180 / 2 = 90
A triangle has 180 degrees. Therefore each side must add to 180. So you are left with ?+?=C The triangle is symmetrical so if cut in half two angles must be the same. Which meant I was looking at 45 + 45 = 90 and 90+90= 180
This assumes Euclidean geometry. If the triangle was, for instance, on the edge of a balloon, the triangle would have fewer than 180 degrees.
A vertical line = 90 and B= 180 so C=90 because
360-90-180= 90
The word measure stopped me dead in my tracks.
From the origin, Vertical lines automatically have a +90 or -270 degree angle associated with them. Horizontal lines have either +180 or -180 degree angle associated with them. 45 degree angled mirror to 135 meeting along the y axis. since the right angle triangle can be assumed as having the corner at the origin, the direction of the line is a matter of which way it's going in your mind. Since I start top, origin, point B, and then back to point C, or "a"... The angle was either 135 or 45.
Third time is the charm.
A+B=C
A+B+C = 180 degrees (angles in a triangle)
If A+B = C then (A+B) must be 90 degrees (any more would result in angle total being over 180 degrees, any less would result in angle total being under 180 degrees)
So 90 degrees + C = 180 degrees
180 degrees - 90 degrees = 90 degrees = C
C = 90 degrees
A +B +C =180° And A+B =C Subsituting , C+C=180° 2C=180 C=90°
∠ A + ∠ B = ∠ C = 1 8 0 − [ ∠ A + ∠ B ]
∠ A + ∠ B = 9 0
Hence, ∠ C = 9 0
(All angles are in degrees)
180 ° ÷ 4 = 4 5
45×2=90 °
Hence the answer is 9 0 °
let angle A =a angle B=b angle C=c given: a+b=c a+b+c=180 c+c=180 2c=180 c=90.
We already know that (\angle A) If we subtract the both equations, we have the following -angle A -angle B +=-
∠A + ∠B + ∠C = 180°: ∠A + ∠B = ∠C ; Then 2∠C = 180°, Therefore, ∠C = 180/2 = 90
By angle sum property of triangle we can say that all angles in a triangle sums up to 180°. It means angle A +angleB+angleC = 180°
Or, angleA + angleB = 180° - angle C [equation 1]
It is given that angleA+angleB = angleC.
Or, 180° - angleC =angle C. [using equ. 1]
Or, 180°= angleC + angleC
Or, 2 angleC = 180°
Or, angleC = 180/2
=90°
I know it is 90, but how to prove it?
180 degrees in a triangle 180/2 =90 90/2 = 45 45 = A and B 45+45=90 90 = C
We know that Angle A + Angle B = Angle C, and that all angles in a triangle add up to 180 degrees regardless of the shape of the triangle (Angle A + Angle B + Angle C = 180 degrees).
So let's substitute Angle C into that second equation replacing "Angle A + Angle B" and solve for Angle C:
Angle C + Angle C = 180 degrees
2 Angle C = 180 degrees
Angle C = 90 degrees
/ _ A + / B + / C = 180 / _ C + / _ C = 180 ( Put / _ A + / _ B = / _ C ) 2/ _ C = 180 / _ C = 90
A+B+C=180, As all angles in triangles do.
So C= A+B and C=180-A-B
Add the equations and get 2C=180 And thus C=90
In a right angle triangle, the only way to add up <A and <B is a 45 45 gives a 90.
The sum of the measures of all three angles of a triangle is always 180°. So,A + B + C = 180°, A + B = 180° - C. Substituting in A + B = C, it gives 180° - C = C, 2C = 180°, C = 90°
It should be a right sngle triangle obviously
If the angle would be obtuse the total sum of angle will go beyond ASP of triangle If the angle would be acute the ASP of triangle would be less than 180 the the only possible outcome is 90
Angle A+angleB= angle C
AngleA+angleB+angleC=180° |angle sum prop.|
As angle A+AngleB=angle C
AngleC+angle C=180°
2(angle C)=180°
Angle C=180°/2
So we get angle C=90° :)
angle A+angle B+angle C= 180 angle A +angle B= angle C therefore , angle C+ angle C= 180 2 x angle C= 180 therefore, angle C= 180/2 =90
Write a solution To assume one triangle.The sum of 3 angels are 180 but the given is A+B=C so to put A&B angel value is 45 then we get c angel is 90
The only way that this equation works is if this is a right triangle. Since c is the largest angle it must be 90 degrees.
Total number of degrees in a triangle equals 180. If A +B +C = 180 and A + B = C we substitute and then have 2C = 180 so C = 90.
45+45=90 45+45+90=180 total measure of angles in a triangle.
In Triangle, all the internal angle sum up to 180 degree. Hence, angle A+B+C= 180. As given, angle A+B=C. So, C+C =180. 2C=180. Hence, C= 90
A+B+C=180 If A+B = C, then 2C=180, therefore C=90
let A=x and B=y Therefore,<A+<B+<C=180 =>2<A+2<B=180 =><A+<B=90 =><C=90
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We know that in a triangle ∠ A + ∠ B + ∠ C = 1 8 0 °
Substituting ∠ A + ∠ B = ∠ C
We have ∠ C + ∠ C = 1 8 0 ° ⟹ ∠ C = 9 0 °