The outer angle of the triangle is 104 degrees, and the inner angles not adjacent to it are such that one is 26 degrees

The outer angle of the triangle is 104 degrees, and the inner angles not adjacent to it are such that one is 26 degrees larger than the other. Find the corners of the triangle.

By the theorem, the external angle is equal to the sum of two internal angles not adjacent to it. This can be proved using the following equations.
Since the sum of the angles of the triangle is 180:
a + b + c = 180 (1);
and the sum of adjacent angles is also 180. Let’s denote the outer adjacent angle as c ‘:
c + c ‘= 180 (2);
Then in equation 1 you can express two angles not adjacent to the angle c ‘:
a + b = 180 – c (3);
We substitute equation 2 in equation 3, expressing from it with:
a + b = 180 – (180 – c ‘);
Let’s simplify this equation:
a + b = 180 – 180 + c ‘;
a + b = c ‘;
We have proved the theorem.
Let x be the first angle, then (x + 26) is the second. Since the total measure of these angles is 104 degrees. Let’s make the equation:
x + x + 26 = 104;
2x = 104 – 26;
2x = 78;
x = 78/2 = 39o is the first corner.
39 + 26 = 65o is the second angle.
Answer: 39o; 65o.