Question

part a
(a) which pair of angles are alternate interior angles?
(b) part b if the value of ∠1 = 60°, find the value of ∠8.

Explanation:

Step1: Recall alternate - interior angles definition

Alternate interior angles are between two parallel lines and on opposite sides of a transversal. In the given figure with parallel lines \(AB\parallel CD\) and transversal \(EF\), \(\angle4\) and \(\angle5\) are alternate interior angles.

Step2: Use angle - relationship for part (b)

\(\angle1\) and \(\angle3\) are vertical angles, so \(\angle3=\angle1 = 60^{\circ}\). \(\angle3\) and \(\angle8\) are corresponding angles. Since \(AB\parallel CD\), corresponding angles are equal. So \(\angle8=\angle3 = 60^{\circ}\).

Answer:

(a) C. \(\angle4\) and \(\angle5\)
(b) D. \(60^{\circ}\)