Question

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 1

When two lines intersect, four angles are formed. Each opposite pair are called vertical angles and are always congruent while each angle with the angle adjacent to it is called linear pair and may not be congruent.

Properties of vertical angles includes:
i.) Vertical angles are always congruent, or of equal measure.
ii.) Both pairs of vertical angles (four angles altogether) always sum to a full angle (360°).

Properties of linear pair includes:
i.) Each pair of linear angles are supplementary (add to 180°).

Answer 2

If you know the measure of one angle in a linear pair, you can find the measure of the other because the sum of the measure of the two angles is 180 degrees. If you know the measure of one angle in a pair of vertical angles, you can find the measure of the other because they are congruent.