How is the angle formed by two chords that intersect in a circle calculated?

The angle formed by two chords that intersect within a circle is calculated as the average of the measures of the arcs intercepted by the angle. When two chords intersect, they divide the circle into arcs. The angle formed between the two chords is equal to half the sum of the measures of the two arcs that are not directly intercepted by the angle in question.

In this case, the correct answer reflects this principle accurately. Specifically, it states that the angle is determined by taking the sum of the measures of the arcs that the chords cut off and then dividing that sum by 2. This gives you the measure of the angle formed at the intersection of the two chords. This relationship arises from properties of circles and the inscribed angle theorem.

Other options do not correctly describe how to find the angle created by the intersection of two chords. For example, one might consider aspects like the direct angles or relationships to oppositional angles, which don't apply to this particular geometrical scenario. Understanding this method allows for practical calculation of angles made by intersecting chords in any circle scenario.