What does an inscribed angle in a circle equal?

An inscribed angle in a circle is defined as an angle formed by two chords in a circle which have a common endpoint. This common endpoint is the vertex of the angle, while the other two endpoints lie on the circle. The critical characteristic of an inscribed angle is that its measure is equal to half the measure of the intercepted arc, which is the arc that lies in the interior of the angle.

This relationship arises because of the way angles relate to arcs in circle geometry. When you draw an angle with its vertex on the circumference of the circle, the arc it subtends — or intercepts — on the circle corresponds directly to this half-measure property. This theorem about inscribed angles is foundational in understanding the relationships between angles and arcs in circles and helps in solving more complex problems involving circles.

The other proposals provided do not accurately represent the properties of inscribed angles. For instance, stating that an inscribed angle equals the complement of the arc does not reflect how inscribed angles relate to arcs in circles. Additionally, claiming that it is twice the intercepted arc contradicts the established theorem, and referring to the circumradius length does not relate to the measurement of angles or arcs at all. Understanding this fundamental relationship is essential for mastering circle the