One of the angles of the triangle is 20 ° larger than the other and 3 times

One of the angles of the triangle is 20 ° larger than the other and 3 times smaller than the third. Find the degree measure of the larger angle of the triangle.

Let us denote by α the value of the first angle of this triangle.

In the initial data for this task, it is reported that this angle is 20 ° more than another angle and 3 times less than the third, therefore, the second angle of this triangle should be equal to α – 20 °, and the third angle – 3α °.

Since the sum of the angles of each triangle is 180 °, we can write the following equation:

α + α – 20 + 3α = 180,

solving which, we get:

5α – 20 = 180;

5α = 180 + 20;

5α = 200;

α = 200/5 = 40 °.

We find the values ​​of the other two angles of the triangle:

α – 20 = 40 – 20 = 20 °;

3α = 3 * 40 = 120 °.

Answer: The larger angle of the triangle is 120 °.