The angles of the triangle are 5: 6: 7. Find these corners. What type does the triangle belong to?

The angles of a triangle add up to 180 degrees. If the angles of a triangle are 5: 6: 7, then this means that the first angle contains 5 parts, the second – 6 of the same parts, and the third – 7 of the same parts of the degree measures of the angle.

Let one part of the angle be x degrees, then the first angle of the triangle is 5x degrees, the second angle is 6x degrees, and the third angle is 7x degrees. By the condition of the problem, it is known that the sum of the angles of a triangle is (5x + 6x + 7x) degrees or 180 °. Let’s make an equation and solve it.

5x + 6x + 7x = 180;

18x = 180;

x = 180: 18;

x = 10 ° – the degree measure of one part;

5x = 10 ° * 5 = 50 ° – the first angle;

6x = 10 ° * 6 = 60 ° – second angle;

7x = 10 ° * 7 = 70 ° is the third angle.

All the corners of the triangle are acute, which means that this triangle will be acute-angled.

Answer. 50 °, 60 °, 70 °.