Question

in the figure below, parallel lines a and b are intersected by a transversal, t. eight angles are formed and are labeled 1 - 8 as shown. use the drop - down arrows to choose the true statement from the first drop - down menu and the reason it is true from the second drop - down menu. (select) (select) angle 2 and angle 4 are congruent angle 1 and angle 8 are congruent angle 5 and angle 8 are supplementary angle 1 and angle 5 are supplementary

Explanation:

Step1: Recall vertical - angle property

Vertical angles are congruent. Angle 2 and angle 4 are vertical angles.

Step2: Recall alternate - exterior - angle property

When two parallel lines are cut by a transversal, alternate - exterior angles are congruent. Angle 1 and angle 8 are alternate - exterior angles.

Step3: Recall linear - pair and corresponding - angle properties

Angle 5 and angle 8 are vertical angles, not supplementary. Angle 1 and angle 5 are corresponding angles, not supplementary.

Answer:

Angle 1 and angle 8 are congruent because of the alternate - exterior angles theorem.