Which of the following statements is true about the measure of an inscribed angle that intercepts an arc on the $unitcircle$?

• A. The measure of the inscribed angle is half the measure of its intercepted arc.
• B. The measure of the inscribed angle is always $90°$.
• C. The measure of the inscribed angle is twice the measure of its intercepted arc.
• D. The measure of the inscribed angle is equal to the measure of its intercepted arc.

Answer: (A)

Verified step by step guidance

1. Recall the definition of an inscribed angle: it is an angle formed by two chords in a circle which have a common endpoint on the circle.
2. Understand that the intercepted arc is the portion of the circle that lies inside the inscribed angle, bounded by the points where the chords intersect the circle.
3. Use the Inscribed Angle Theorem, which states that the measure of an inscribed angle is exactly half the measure of its intercepted arc.
4. Express this relationship mathematically as: \(\text{Measure of inscribed angle} = \frac{1}{2} \times \text{Measure of intercepted arc}\).
5. Note that this means the inscribed angle is not always less than 90°, nor is it equal to or twice the intercepted arc; it is always half the intercepted arc's measure.