Imagine two lines intersect. How can the properties of linear pairs and vertical angles help to determine the angle measures created by the intersecting lines? Explain.

Answer:

When two lines intersect, they form linear pairs and vertical angles. The angles in a linear pair are supplementary, meaning their measures add up to 180 degrees. Therefore, if you know the measure of one angle, you can find its linear pair by subtracting from 180. Vertical angles are congruent, so their measures are equal. By using these two properties, knowing just one angle measure allows you to determine the measures of all four angles created by the intersection.