The outside angle of a triangle is 140 degrees, and the inside corners not adjacent to it are 3: 4.

The outside angle of a triangle is 140 degrees, and the inside corners not adjacent to it are 3: 4. Find all the inside corners of the triangle.

It is known from the condition that the outer angle of the triangle is 140 °, and the inner angles that are not adjacent to it are related as 3: 4.

Let’s remember the property of the external angle, it says that the external angle of a triangle is equal to the sum of two angles of the triangle that are not adjacent to it.

Let’s introduce the coefficient of similarity x and write down the degree measures of our angles 3x and 4x.

So the sum of the angles that are related as 3: 4 is 140 °.

Let’s compose and solve the equation.

3x + 4x = 140;

7x = 140;

x = 20;

3x = 20 * 3 = 60 °;

4x = 4 * 20 = 80 °.

The third inner corner is 180 – (60 + 80) = 40 °.