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.

Explanation:

When two lines intersect, linear pairs of angles are supplementary (sum to \(180^{\circ}\)). Vertical angles are congruent (equal in measure). If one angle measure is known, use the linear - pair property (\(\angle1+\angle2 = 180^{\circ}\)) to find an adjacent angle. Then, use the vertical - angle property (\(\angle1=\angle3\), \(\angle2=\angle4\)) to find the remaining angles.

Answer:

First, use the linear - pair property (supplementary angles) for adjacent angles. Then, use the vertical - angle property (congruent angles) for non - adjacent angles.