Find the largest angle of a triangle if its angles are proportional to the numbers 5,6,7

We are given a triangle, and we also know that the angles of a triangle are proportional to the numbers 5: 6: 7. To find the largest angle, we start by writing and solving an equation.

Let us apply the theorem on the sum of the angles of a triangle to solve. It says that the sum of the angles of a triangle is 180 °.

We enter the coefficient of similarity k and write down the degree measure of the angles as 5k, 6k and 7k.

We get the equation:

5k + 6k + 7k = 180;

k (5 + 6 + 7) = 180;

18k = 180;

k = 10.

The angles will have a degree measure of 5 * 10 = 50 °, 6 * 10 = 60 °, 7 * 10 = 70 °.

Answer: 70 °.