Find the angles of a triangle if you know that the sum of two angles is 80 degrees and one of them

Find the angles of a triangle if you know that the sum of two angles is 80 degrees and one of them is less than the other by 20 degrees.

Let’s denote these angles of the triangle through x and y.

According to the condition of the problem, the sum of these two angles is 80 °, therefore, we can write the following ratio:

x + y = 80.

It is also known that one of these angles is less than the other by 20 degrees, therefore, we can write the following ratio:

x = y + 20.

We solve the resulting system of equations.

Substituting into the first equation the value x = y + 20 from the second equation, we get:

y + 20 + y = 80;

2y + 20 = 80;

2y = 80 – 20;

2y = 60;

y = 60/2;

y = 30 °.

Knowing y, we find x:

x = y + 20 = 30 + 20 = 50 °.

To find the third angle of this triangle, we will use the fact that the sum of the angles of the triangle is 180 °.

Therefore, the value of the third angle of this triangle is:

180 – 50 – 30 = 180 – 80 = 100 °.

Answer: The angles of this triangle are 30 °, 50 ° and 100 °.