Question

in circle o, $overline{ae}$ and $overline{fc}$ are diameters. arc ed measures 17°. what is the measure of $overline{efc}$? 107° 180° 253° 270°

Explanation:

Step1: Recall circle - arc property

The measure of a semi - circle is 180°. Since $\overline{FC}$ is a diameter, arc $FEC$ is a semi - circle with measure 180°.

Step2: Calculate measure of arc $EFC$

Arc $EFC$ is the major arc. The sum of the measures of the arcs of a circle is 360°. Arc $ED$ measures 17°. Arc $DC$ is part of the semi - circle $FEC$. We know that arc $FEC = 180^{\circ}$.
The measure of arc $EFC=360^{\circ}-\text{measure of arc }ED$.
\[

$$\begin{align*} \text{measure of arc }EFC&=360 - 17\\ &=253^{\circ} \end{align*}$$

\]

Answer:

253°