A symmetric triangle!

Geometry Level 1

Triangle A B C ABC has the property that A + B = C \angle A+\angle B= \angle C . Find the measure of C \angle C in degrees.


The answer is 90.

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42 solutions

Parth Lohomi
Jun 4, 2015

We know that in a triangle A + B + C = 180 ° \angle A+\angle B+\angle C=180°

Substituting A + B = C \angle A+\angle B =\angle C

We have C + C = 180 ° C = 90 ° \angle C+\angle C=180°\implies \angle C=\boxed{90°}

Well, in an Euclidean geometry, this is true, but not in general

Patrick Bourg - 5 years, 6 months ago

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.

Ethen Handy - 5 years, 12 months ago

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What about a 30-60-90?... Or other combinations?

tina ayers - 5 years, 12 months ago

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You are right....There can be all sorts of P & C for A+B=90.

Govind Menon - 5 years, 12 months ago

I put 91 ans got it wrong. 91+44.5+44.5= 180. ????

Garrison Wynn - 5 years, 6 months ago

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44.5+44.5 ≠ 91

Henk Elemans - 5 years, 6 months ago
Franklin Okeme
Jun 14, 2015

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.

Garrett Rasnick - 6 years ago

Did you have to do it so long?

Saswata Saha - 5 years, 12 months ago

Congratulations- you just broke maths

Garrison Wynn - 5 years, 6 months ago

A+B =C so, C+C=180 2C=180 C=90

Nihal Lakhani
Jun 9, 2015

The only case possible is, the triangle should be right angle triangle

Can you prove there are no other cases?

Jake Lai - 6 years ago

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Can you proove to disproove ?

siddharth bhatt - 6 years ago

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I'm assuming you mean "can you disprove it," in which case, can you disprove that unicorns exist?

No Name - 5 years, 12 months ago
Jc DelaPaz
Jun 7, 2015

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.

Franklin Okeme - 6 years ago
Lauren Rose
Jun 12, 2015

A+B=C therefore C+C=180 180 / 2 = 90

Georgina Phillips
Jun 10, 2015

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

Andrew Becker
Nov 19, 2015

This assumes Euclidean geometry. If the triangle was, for instance, on the edge of a balloon, the triangle would have fewer than 180 degrees.

Winston Lyle
Jun 14, 2015

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.

Nathan Jeffs
Jun 13, 2015

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

Aviral Srivastava
Jun 10, 2015

A +B +C =180° And A+B =C Subsituting , C+C=180° 2C=180 C=90°

Prabhnoor Singh
Apr 12, 2020

A + B = C = 180 [ A + B ] \angle A + \angle B = \angle C = 180 - [\angle A + \angle B]

A + B = 90 \angle A + \angle B = 90

Hence, C = 90 \angle C = 90

(All angles are in degrees)

Minor Major
Nov 11, 2018

used 30,60,90 triangles

Matin Naseri
Jan 24, 2018

180 ° ÷ 4 = 45 \text{180}^{°}÷4=45

45×2=90 ° \text{45×2=90}^{°}

Hence the answer is 90 ° \boxed{90}^{°}

Shinekhuu Nory
Jan 6, 2017

180/4=45 45*2=90

Rati Nair
Aug 24, 2016

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.

Mario Ernesto
Jul 12, 2016

We already know that (\angle A) If we subtract the both equations, we have the following -angle A -angle B +=-

Adli Mizan
Jun 7, 2016

Well this is kacang goreng

Sadasiva Panicker
Nov 19, 2015

∠A + ∠B + ∠C = 180°: ∠A + ∠B = ∠C ; Then 2∠C = 180°, Therefore, ∠C = 180/2 = 90

Kathakali Mitra
Jul 1, 2015

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°

C X
Jun 30, 2015

I know it is 90, but how to prove it?

Paul Donikowski
Jun 14, 2015

180 degrees in a triangle 180/2 =90 90/2 = 45 45 = A and B 45+45=90 90 = C

Steve Jackson
Jun 14, 2015

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

Hitesh Parmar
Jun 14, 2015

/ _ A + / B + / C = 180 / _ C + / _ C = 180 ( Put / _ A + / _ B = / _ C ) 2/ _ C = 180 / _ C = 90

Jordan Dock
Jun 14, 2015

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

Shehan Melanka
Jun 14, 2015

Isn't it obvious????

Nada Abdelaziz
Jun 14, 2015

In a right angle triangle, the only way to add up <A and <B is a 45 45 gives a 90.

Swayam Kumar
Jun 14, 2015

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°

Dhani Para
Jun 14, 2015

It should be a right sngle triangle obviously

Dhruvit Arora
Jun 14, 2015

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

Aditi Mishra
Jun 14, 2015

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° :)

Vaibhav Raj
Jun 13, 2015

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

Asha Gupta
Jun 13, 2015

A+B+C=180, 2C=180 , so C=90.

Deepak Raj
Jun 13, 2015

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

Earle M'Lean
Jun 13, 2015

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.

Joshua Fiddler
Jun 13, 2015

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.

Jay Rajpra
Jun 13, 2015

180/2 = 90

Cheryl Manzano
Jun 13, 2015

45+45=90 45+45+90=180 total measure of angles in a triangle.

Jia Agarwal
Jun 11, 2015

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

Archil Patel
Jun 7, 2015

2angleC=180 Angle C =90

Chirantan Biswas
Jun 4, 2015

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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