One of the outer angles of the triangle is 120 degrees, it is known that one of the inner angles that are not adjacent

One of the outer angles of the triangle is 120 degrees, it is known that one of the inner angles that are not adjacent to it is 2 times larger than the other. Find the degree measure of the larger of these angles.

The sum of adjacent angles is 180 °. Find the inner corner of a triangle if its adjacent outer corner is known:

180 ° – 120 ° = 60 °.

The sum of the angles in any triangle is always 180 °. Let’s solve the problem using the equation, where:

x is the first corner of the triangle;

2x – the second corner of the triangle (since it is twice as large as the first);

Let’s compose and solve the equation:

x + 2x + 60 = 180;

3x + 60 = 180;

3x = 180 – 60;

3x = 120;

x = 120/3;

x = 40 ° – the first corner of the triangle;

2x = 2 * 40 = 80 ° is the second and largest corner of the triangle.

Answer: 80 °