Angles of a triangle as 2; 3; 4. Find the ratio of the outer corners of the triangle.

Let’s find what the angles of this triangle are equal to.

Let’s denote by x half the size of the smallest angle of this triangle.

Then the smallest angle of the triangle will be 2x.

According to the condition of the problem, the angles of this triangle are related as 2: 3: 4, therefore, the values ​​of the other two angles of this triangle will be equal to 3x and 4x.

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

2x + 3x + 4x = 180,

solving which, we get:

9x = 180;

x = 180/9;

x = 20.

Therefore, the angles of this triangle are 2 * 20 = 40 °, 3 * 20 = 60 ° and 4 * 20 = 80 °.

Then the outer angles of this triangle are 180 – 40 = 140 °, 180 – 60 = 120 ° and 180 – 80 = 100 ° and they are related as 140: 120: 100 or as 7: 6: 5.

Answer: The outer corners of this triangle are in the 7: 6: 5 ratio.