Final answer:
The four angles formed by the intersection of two lines, when one angle is 42 degrees, are two angles of 42 degrees and two angles of 138 degrees due to the properties of vertical and supplementary angles.
Step-by-step explanation:
When two lines intersect, they form four angles. Given that one of the angles measures 42 degrees, we can determine the measures of the other three angles using properties of intersecting lines.
Opposite angles, also known as vertical angles, are equal. Therefore, the angle opposite the 42-degree angle also measures 42 degrees. The adjacent angles to the 42-degree angle are supplementary to it because straight lines measure 180 degrees. This means that each of the adjacent angles is 138 degrees (180 - 42 = 138).
In conclusion, the four angles formed by the intersection of two lines with one angle measuring 42 degrees are 42 degrees, 138 degrees, 42 degrees, and 138 degrees.