Question

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

Explanation:

Step1: Recall circle - arc property

The measure of a full - circle arc is 360°.

Step2: Identify known arcs

Since $\overline{AE}$ and $\overline{FC}$ are diameters, arc $EFC$ and arc $EAF$ together make up the whole circle. Also, we know that arc $ED = 17^{\circ}$, and the angle at the center corresponding to the right - angle formed by the diameters is 90°.

Step3: Calculate the measure of arc $EFC$

The measure of arc $EFC=360^{\circ}-$ (measure of arc $ED + 90^{\circ}$).
The measure of arc $EFC = 360-(17 + 90)=253^{\circ}$.

Answer:

253°