It is known that the values of the angles A, B, C of the triangle ABC are 6: 5: 7, respectively. Find the degree measure of angle A.

We know that the degree measures of the angles of the triangle are 6: 5: 7. We need to find the degree measure of the first angle.

In order to find it, we will compose and solve a linear equation. And we will start by introducing the coefficient of similarity k.

Now the degree measures of angles can be written as:

6k; 5k and 7k.

Based on the fact that the sum of the angles of the triangle is 180 °, we get the equation:

6k + 5k + 7k = 180;

k (6 + 5 + 7) = 180;

18k = 180;

k = 180: 18;

k = 10.

Now we can calculate the degree measure of the first angle.

6 * 10 = 60 °.