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

Linear pairs are adjacent angles that are supplementary.
Their measures add to 180 deg.
Vertical angles are congruent.

Let's say two lines intersect, and you know the measure of one of the 4 angles that were formed. One angle measures k degrees. You can find all the other measures.
Since one angle measures k degrees, the angle vertical to it also measures k degrees.
Each of the other two angles forms a linear pair with the angle that measures k. That means each angle is supplementary to the angle measuring k degrees and has a measure of (180 - k) degrees.

Ineed with this same question!

Answercounterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axisexplanationthe given figure has verticesrecall that for counterclockwise rotation about the origin, when we rotate figure pqrs counterclockwise through an angle of 180° about the origin, the coordinates will becomenext, we reflect in the y-axis by negating the x-coordinates of the resulting figure to obtain,therefore the correct answer is c