One of the outer corners of the triangle is 120 °, and the difference between the inner angles not adjacent to it is 30 °.

One of the outer corners of the triangle is 120 °, and the difference between the inner angles not adjacent to it is 30 °. Determine the larger inner corner of the triangle.

From the condition, we know that one of the outer angles of the triangle is 120 °, and it is also said that the difference between two angles not adjacent to it is 30 °.

Let’s remember the property of the outer corner of a triangle.

The outer angle of a triangle is equal to the sum of two angles of the triangle that are not adjacent to it.

Let’s denote by the variable x one of the angle not adjacent to the outer corners of the triangle, then the second non-adjacent angle is (x + 30).

Let’s compose and solve the equations:

x + x + 30 = 120;

2x = 120 – 30;

2x = 90;

x = 45 ° – one of the corners of the triangle, 45 + 30 = 75 ° – the second angle; 180 – 120 = 60 ° third corner of the triangle.

Answer: 75 °