In a circle, what is the measure of an inscribed angle that subtends arc AB equal to half the measure of the central angle subtending the same arc?

• A. Equals half the measure of its intercepted arc.
• B. Equals the measure of the central angle
• C. Equals the measure of arc AB
• D. Equals double the measure of the intercepted arc

Answer: (A)

The inscribed angle theorem says that an angle formed by two chords intercepting an arc has a measure equal to half the measure of that intercepted arc. Since the central angle subtending the same arc has a measure equal to the arc’s measure, the inscribed angle is also half of that central angle. So the inscribed angle equals half the intercepted arc’s measure (and also half the central angle’s measure for the same arc). For example, if arc AB measures 80 degrees, the inscribed angle subtending AB is 40 degrees, while the central angle subtending AB is 80 degrees.