Question

october 27 at 8:00 am
answer attempt 8 out of 99
angle 1 & angle 7, and angle 2 & angle 8 are pairs of angles. these angles are congruent. these angles supplementary.
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Explanation:

Step1: Recall angle - pair definitions

Corresponding angles are in the same relative position. Alternate - exterior angles are outside the two lines and on opposite sides of the transversal. Angle \(1\) and angle \(7\), angle \(2\) and angle \(8\) are alternate - exterior angles.

Step2: Recall congruent and supplementary angle properties

By the alternate - exterior angles theorem, alternate - exterior angles are congruent.
For supplementary angles, the sum of two supplementary angles is \(180^{\circ}\). Since alternate - exterior angles are congruent, if \(\angle1=\angle7\) and \(\angle2 = \angle8\), and \(\angle1+\angle2=180^{\circ}\) (linear pair), then \(\angle7+\angle8 = 180^{\circ}\) (by substitution).

Answer:

Angle \(1\)&Angle \(7\), and Angle \(2\)&Angle \(8\) are pairs of alternate - exterior angles. These angles are always congruent. These angles are sometimes supplementary.