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 °.
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