Question

give a pair of alternate exterior angles, a pair of corresponding angles, and a pair of alternate interior angles. (a) alternate exterior angles: ∠ and ∠ (b) corresponding angles: ∠ and ∠ (c) alternate interior angles: ∠ and ∠ try one last time

Explanation:

Step1: Recall angle - pair definitions

Alternate exterior angles are outside the two parallel lines and on opposite sides of the transversal. Corresponding angles are in the same relative position with respect to the parallel lines and the transversal. Alternate interior angles are between the two parallel lines and on opposite sides of the transversal.

Step2: Identify alternate exterior angles

For the given parallel lines \(g\) and \(h\) cut by transversal \(m\), \(\angle1\) and \(\angle7\) are alternate exterior angles.

Step3: Identify corresponding angles

\(\angle2\) and \(\angle6\) are corresponding angles as they are in the same relative position above the parallel lines and on the same side of the transversal.

Step4: Identify alternate interior angles

\(\angle3\) and \(\angle5\) are alternate interior angles as they are between the parallel lines and on opposite sides of the transversal.

Answer:

(a) \(\angle1\) and \(\angle7\)
(b) \(\angle2\) and \(\angle6\)
(c) \(\angle3\) and \(\angle5\)