The angles of a triangle are in arithmetic progression. Find the largest angle of a triangle

The angles of a triangle are in arithmetic progression. Find the largest angle of a triangle if its smallest angle is 120 degrees.

Let us denote by x the difference of that arithmetic progression, which is formed by the three angles of a given geometric figure.

In the initial data for this task, it is reported that the smallest angle is 20 degrees.

Then the other two angles of this triangle should be 20 + x and 20 + 2x degrees, respectively.

Since the sum of the values ​​of all 3 angles of a triangle is always 180 °, we can draw up the following equation:

20 + 20 + x + 20 + 2x = 180,

solving which, we get:

60 + 3x = 180;

(60 + 3x) / 3 = 180/3;

20 + x = 60;

x = 60 – 20 = 40.

Find the largest angle:

20 + 2x = 20 + 2 * 40 = 20 + 80 = 100 °.

Answer: 100 °.