An inscribed angle has its vertex on a ______ and its sides are ______.

An inscribed angle is formed when its vertex lies on the circumference of a circle, and its sides are represented by chords of that circle. This geometric figure is fundamental in understanding the properties of circles and their angles.

The defining features of an inscribed angle are crucial: with the vertex positioned on the circle, the two sides of the angle extend toward and connect with points on the circumference (these connections are the chords). A key property of inscribed angles is that the measure of the angle is half the measure of the intercepted arc that lies between the endpoints of the chords forming the angle.

Understanding this concept is essential when solving problems related to angles and circles in surveying and geometry, as it lays the groundwork for further exploration of circular properties, relationships, and the measures of angles.