Fundamentals of Surveying (FS) Practice Exam

An inscribed angle is measured by what portion of its intercepted arc?

1. One-third

2. One-half

3. Two-thirds

4. One-quarter

The correct answer is: One-half

An inscribed angle is defined as an angle formed by two chords in a circle that originate from a common endpoint on the circle's circumference. The critical property of an inscribed angle is that it is always measured by half the degree measure of its intercepted arc. The intercepted arc is the portion of the circumference that lies between the two endpoints of the angle on the circle. In simpler terms, if you have an inscribed angle that intercepts an arc measuring, for example, 60 degrees, then the inscribed angle itself will measure 30 degrees, which is half of that intercepted arc. This relationship holds true for any size of arc and is a fundamental property of circles and angles. Understanding this property is useful not only in geometry but also in surveying, where angles and their measurements can be critical for determining locations and creating maps. Hence, an inscribed angle is always measured by one-half of its intercepted arc.