Question

Question was provided via image upload.

Explanation:

Step1: Recall the definitions

• Alternate - interior angles: They are non - adjacent angles that lie between the two lines and on opposite sides of the transversal.
• Corresponding angles: They are in the same relative position with respect to the two lines and the transversal.
• Alternate - exterior angles: They are non - adjacent angles that lie outside the two lines and on opposite sides of the transversal.

Step2: Identify the pairs

• For alternate - interior angles (\(a\)): \(\angle4\) and \(\angle6\), \(\angle3\) and \(\angle5\)
• For corresponding angles (\(b\)): \(\angle1\) and \(\angle5\), \(\angle2\) and \(\angle6\), \(\angle3\) and \(\angle7\), \(\angle4\) and \(\angle8\)
• For alternate - exterior angles (\(c\)): \(\angle1\) and \(\angle7\), \(\angle2\) and \(\angle8\)

Answer:

(a) \(\angle4\) and \(\angle6\), \(\angle3\) and \(\angle5\)
(b) \(\angle1\) and \(\angle5\), \(\angle2\) and \(\angle6\), \(\angle3\) and \(\angle7\), \(\angle4\) and \(\angle8\)
(c) \(\angle1\) and \(\angle7\), \(\angle2\) and \(\angle8\)