The difference between the two angles formed at the intersection of two straight lines is 42 degrees. Find all the angles formed.

1. Let’s denote the degree measure of the smaller angle through x.

2. Determine the degree measure of the larger angle:

(x + 42˚)

3. Since the sum of adjacent angles is 180˚, we compose and solve the equation:

(x + 42˚) + x = 180˚;

x + 42˚ + x = 180˚;

2x + 42˚ = 180˚;

2x = 180˚ – 42˚;

2x = 138˚;

x = 138˚: 2;

x = 69˚.

4. The degree measure of the smaller angle is x = 69˚.

5. What is the degree measure of the larger angle?

x + 42˚ = 69˚ + 42˚ = 111˚.

6. As you know, the vertical angles are equal, so the large angles formed at the intersection of two straight lines will be equal to 111˚, and the smaller angles will be equal to 69˚.

Answer: the degree measures of the angles formed at the intersection of two straight lines are equal to 111˚, 69˚, 111˚, 69˚.