Question

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

Explanation:

Step1: Identify right angle arc

Since $\overline{OD} \perp \overline{FC}$, arc $DC$ is $90^\circ$.

Step2: Find arc EC

Arc $EC = \text{arc } ED + \text{arc } DC = 17^\circ + 90^\circ = 107^\circ$

Step3: Calculate arc EFC

A full circle is $360^\circ$, so $\text{arc } EFC = 360^\circ - \text{arc } EC = 360^\circ - 107^\circ = 253^\circ$

Answer:

253°