The sum of the vertical angles is 20 degrees less than the angle adjacent to each one. Find the degree measures of these vertical angles.

1. Let’s denote the degree measure of the vertical angle through x.
2. Let’s define the degree measure of the adjacent angle:
(180˚ – x).
3. Let’s compose and solve the equation:
2x + 20˚ = 180˚ – x;
3x + 20˚ = 180˚;
3x = 180˚ – 20˚;
3x = 160˚;
x = 160˚: 3;
x = 53 1 / 3˚.
4. The degree measure of the vertical angle is x = 53 1 / 3˚.
Answer: the degree measures of the vertical angles are 53 1 / 3˚, 53 1 / 3˚.