Question

by which angle must \\(\boldsymbol{\overline{ab}}\\) turn about point a in the clockwise direction so that it coincides with \\(\boldsymbol{\overline{ae}}\\)?

a. \\(90^\circ\\)

b. \\(180^\circ\\)

c. \\(270^\circ\\)

d. \\(360^\circ\\)

Explanation:

Step1: Analyze the positions of \(\overline{AB}\) and \(\overline{AE}\)

\(\overline{AB}\) is along the negative x - axis, and \(\overline{AE}\) is along the positive x - axis. The angle between the negative x - axis and the positive x - axis is a straight angle.

Step2: Determine the clockwise rotation angle

A straight angle has a measure of \(180^{\circ}\). So, to rotate \(\overline{AB}\) about point A in the clockwise direction to coincide with \(\overline{AE}\), the angle of rotation is \(180^{\circ}\).

Answer:

B. \(180^{\circ}\)