The sum of the vertical angles is 5 times less than the angle adjacent to each of them. Find these vertical angles.

Let’s denote by x the value of one of these vertical angles.

Since the vertical angles are always equal to each other, the second vertical angle is also x.

Since adjacent angles always add up the unfolded angle, the value of the angle adjacent to any of these vertical angles is 180 – x.

According to the condition of the problem, the sum of these vertical angles is 5 times less than the angle adjacent to each of them, therefore, we can compose the following equation:

x + x = (180 – x) / 5.

Solving this equation, we get:

2x = (180 – x) / 5;

5 * 2x = 180 – x;

10x + x = 180;

11x = 180;

x = 180/11;

x = 16 4/11 °.

Answer: These vertical angles are 16 4/11 °.