An inscribed angle is an angle formed by two chords in a circle that share an endpoint. This endpoint is called the vertex of the angle, while the other endpoints of the chords lie on the circumference of the circle. The measure of an inscribed angle is always half the measure of the arc that it intercepts. For example, if an inscribed angle intercepts an arc measuring 80 degrees, the inscribed angle itself measures 40 degrees. This property is useful in various geometric problems and is a fundamental concept in circle geometry, often studied in relation to other figures like triangles and polygons.