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

August 30, 2021 | education

| 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˚.

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