Question 1

Question

Question
During a recent bike ride, the chain on Elena’s bicycle slipped off the rear gear. In order to reattach the chain, she turned her bicycle upside-down and placed the loose chain on top of the rear gear. She used the pedal to slowly rotate the tire

of one complete rotation to reattach the chain, as shown by the arrow in the following figure.

The figure presents a diagram of a circular bicycle wheel. One line segment extends vertically upward from the center of the circle, and one line segment extends downward and to the right from the center of the circle. A curved arrow extends clockwise from the vertical line segment to the slanted line segment, along the path of the circle.
What is the measure of the central angle of this rotation?

Responses

Answer A: 45 degrees
A

Answer B: 67.5 degrees
B

Answer C: 120 degrees
C

Answer 1

To determine the measure of the central angle for one complete rotation of the rear gear when Elena pedals the bicycle, we need to understand the relationship between the rotation of the pedal and the movement of the chain on the rear gear.

Given that the chain goes back onto the rear gear during a complete rotation of the tire, the relevant angle in the scenario is that of the complete circle. A complete rotation of any circle is \(360\) degrees.

Since the problem implies that she rotated the pedal such that the chain reattached completely, it leads us to conclude that the central angle corresponding to the rotation of one complete revolution of the rear gear is \(360\) degrees.

However, the responses provided (45 degrees, 67.5 degrees, and 120 degrees) do not include \(360\) degrees. It's possible that the angle might refer to a smaller section or might be confused with a fraction of the complete rotation.

Due to the lack of clarity in the question and the options at hand, it seems that it might be suggesting to analyze smaller section angles instead. However, for typical scenarios of chain problems on bikes in similar contexts, the question seems incorrectly formed.

In summary, the measure of the central angle of this rotation should correspondingly be \(360\) degrees for a complete rotation. But since it's not an option, there may be an error or additional context needed to select one of the provided angles (A, B, or C). If the question intended to ask about a fraction of the circle, please revise that context.