By the arc definition, the degree of curve is the central angle that subtends a 100 ft _____.

The degree of curve in surveying is defined based on the relationship between an arc and its subtended angle. When it states that the degree of curve is the central angle that subtends a 100 ft arc, it highlights a key geometric concept used in road and railroad design, where curves are created for safe navigation.

This definition means that if you have a curve along a road or track, you can describe that curve's sharpness or gentleness by how sharply it turns, indicated by the degree of curve. Specifically, for a 100 ft chord (the straight line connecting the endpoints of the arc), the angle at the center of the circular path formed by the arc is the essential measure that describes the degree of curvature. The 100 ft length is significant because it standardizes the measurement, allowing for comparison between curves of different radii.

The other options do not fit the definition as closely. For example, referring to a line would imply a straight path, which does not relate to curvature. A triangle is not pertinent to the concept of a curve, and while radius is involved in the geometry of circles, it does not represent the specific physical property being quantified when discussing degrees of curvature. Therefore, the arc definition focused on the relationship between the