in circle o, $overline{ae}$ and $overline{fc}$ are diameters. arc ed measures 17°. what is the measure of…

Explanation:

Step1: Recall circle - arc properties

The sum of the measures of the arcs of a circle is 360°. A diameter divides a circle into two semi - circles, and the measure of a semi - circle is 180°.

Step2: Identify related arcs

Since (\overline{AE}) and (\overline{FC}) are diameters, arc (EFC) and arc (EAC) are semi - circles. Also, arc (EAC) can be written as the sum of arc (ED), arc (DC), and arc (CA). We know that (\angle EOD = 17^{\circ}) (the central angle is equal to the measure of the intercepted arc), and (\angle DOC=90^{\circ}) (given by the right - angle in the figure), and arc (CA) is a semi - circle with measure 180°.

Step3: Calculate the measure of arc (EFC)

The measure of arc (EFC=360^{\circ}-\text{measure of arc } EAC). First, find the measure of arc (EAC). Arc (EAC=\text{arc }ED+\text{arc }DC+\text{arc }CA). Arc (ED = 17^{\circ}), arc (DC = 90^{\circ}), and arc (CA=180^{\circ}), so arc (EAC=17^{\circ}+90^{\circ}+180^{\circ}=287^{\circ}). Then, arc (EFC = 360^{\circ}-287^{\circ}=253^{\circ}).

Answer:

253°