Question

angle relationships
points e, f, and d are located on circle c.
the measure of arc ed is 68°. what is the measure of angle efd?
112°
34°
68°
132°

Explanation:

Step1: Use the inscribed - angle theorem

The inscribed - angle theorem states that an inscribed angle is half of the measure of the central angle that subtends the same arc. Also, an inscribed angle is half of the measure of the arc it subtends.

Step2: Identify the arc and the inscribed angle

We are given that the measure of arc \(ED\) is \(m\overset{\frown}{ED}=68^{\circ}\). The angle \(\angle EFD\) is an inscribed angle that subtends arc \(ED\).

Step3: Calculate the measure of \(\angle EFD\)

By the inscribed - angle theorem \(m\angle EFD=\frac{1}{2}m\overset{\frown}{ED}\). Substitute \(m\overset{\frown}{ED} = 68^{\circ}\) into the formula: \(m\angle EFD=\frac{1}{2}\times68^{\circ}\).

Answer:

\(34^{\circ}\)