Given that line segment $su$ is a diameter of circle $v$, what is the measure of the arc subtended by an inscribed angle of $56°$?

• A. $56°$
• B. $68°$
• C. $163°$
• D. $112°$

Answer: (D)

Verified step by step guidance

1. Recall the Inscribed Angle Theorem, which states that an inscribed angle in a circle is half the measure of the arc it subtends. Mathematically, if an inscribed angle measures \(\theta\), then the arc it subtends measures \$2\theta$.
2. Identify the given inscribed angle measure, which is \$56^\circ$ in this problem.
3. Apply the Inscribed Angle Theorem formula: multiply the inscribed angle by 2 to find the measure of the arc. So, calculate \$2 \times 56^\circ$.
4. Understand that since \(su\) is a diameter of the circle, the arc subtended by the inscribed angle is not the entire circle but the specific arc opposite the angle, which corresponds to the doubled angle measure.
5. Conclude that the measure of the arc subtended by the inscribed angle is \$112^\circ$, which is twice the inscribed angle measure.