Question

points e, f, and d are located on circle c. the measure of arc ed is 68°. what is the measure of angle efd?

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Apply the theorem

Angle \(EFD\) is an inscribed angle that intercepts arc \(ED\). Given that the measure of arc \(ED\) is \(m\overset{\frown}{ED}=68^{\circ}\). Let the measure of angle \(EFD\) be \(x\). By the inscribed - angle theorem \(x = \frac{1}{2}m\overset{\frown}{ED}\).
Substitute \(m\overset{\frown}{ED}=68^{\circ}\) into the formula: \(x=\frac{1}{2}\times68^{\circ}\).

Answer:

\(34^{\circ}\)