Question

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

Explanation:

Step1: Identify alternate - interior angles

Alternate - interior angles are between the two parallel lines and on opposite sides of the transversal. For lines \(a\) and \(b\) cut by transversal \(m\), \(\angle2\) and \(\angle7\) are alternate - interior angles.

Step2: Identify alternate - exterior angles

Alternate - exterior angles are outside the two parallel lines and on opposite sides of the transversal. So, \(\angle1\) and \(\angle8\) are alternate - exterior angles.

Step3: Identify corresponding angles

Corresponding angles are in the same relative position with respect to the parallel lines and the transversal. \(\angle1\) and \(\angle5\) are corresponding angles.

Answer:

(a) \(\angle2\) and \(\angle7\)
(b) \(\angle1\) and \(\angle8\)
(c) \(\angle1\) and \(\angle5\)