Given that the measure of arc ED is $68°$, what is the measure of angle EFD if angle EFD is an inscribed angle that intercepts arc ED?

• A. $68°$
• B. $132°$
• C. $112°$
• D. $34°$

Answer: (D)

Verified step by step guidance

1. Recall the definition of an inscribed angle: an inscribed angle is an angle formed by two chords in a circle which have a common endpoint. The vertex of the angle lies on the circle, and the angle intercepts an arc.
2. Understand the key property of inscribed angles: the measure of an inscribed angle is exactly half the measure of the intercepted arc.
3. Identify the given information: the measure of arc ED is \$68^\circ$, and angle EFD is an inscribed angle intercepting this arc.
4. Apply the inscribed angle theorem formula: if \(\angle EFD\) intercepts arc \(ED\), then \(\angle EFD = \frac{1}{2} \times \text{measure of arc } ED\).
5. Substitute the given arc measure into the formula: \(\angle EFD = \frac{1}{2} \times 68^\circ\) to find the measure of angle EFD.