**What are the angles of the triangle ABC, if the sum of the angles A and B is equal to 100 degrees, the sum of the angles B and C equal to 120 degrees?**

The triangle and the angles |

**We have two sum of two angles:**

A + B = 100

B + C = 120

The sum of angles in a triangle is 180 degrees.

A + B + C = 180

Substitute in this formula the sum of two angles and find the third angle:

100 + C = 180

C = 180 - 100

C = 80

The second sum of the angles substitute angle C:

B + 80 = 120

B = 120 - 80

B = 40

The first sum of angles substitute angle B:

A + 40 = 100

A = 100 - 40

A = 60

A: The angles of the triangle are equal: A=60 degrees, B=40 degrees, C=80 degrees.

If we substitute in the second sum angles of a triangle, then the solution would be:

A + 120 = 180

A = 180 - 120

A = 60

60 + B = 100

B = 100 - 60

B = 40

60 + 40 + C = 180

C = 180 - 60 - 40

C = 80

The third variant of the decision:

We find the angle A of the first sum.

A + B = 100

A = 100 - B

We find the angle C of the second sum.

B + C = 120

C = 120 - B

Substitute the found angles to the general formula:

A + B + C = 180

(100 - B) + B + (120 - B) = 180

100 - B + B + 120 - B = 180

B - 2B = 180 - 100 - 120

-B = -40

B = 40

A = 100 - 40

A = 60

C = 120 - 40

C = 80

Conclusion: if the problem is solved correctly, the result does not depend on the method of solution.