An inscribed angle is measured as what fraction of its intercepted arc?

The inscribed angle theorem states that an inscribed angle is always half the measure of its intercepted arc. This means that if you have an arc defined by two points on the circumference of a circle, the inscribed angle that subtends that arc will be measured as one-half the angular measurement of the arc itself.

For example, if the intercepted arc measures 80 degrees, the inscribed angle that subtends this arc would measure 40 degrees. This relationship holds true for any inscribed angle and its corresponding arc.

Understanding this theorem is fundamental in surveying and geometry because it allows surveyors to make accurate calculations related to angular measurements when working with circular features, such as in the design and layout of roads, highways, and other infrastructure components.