Question

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

Explanation:

Step1: Recall the total degrees in a circle

A full - circle has \(360^{\circ}\).

Step2: Find the measure of the arc opposite to \(\widehat{EFC}\)

The arc opposite to \(\widehat{EFC}\) is \(\widehat{EDC}\). Since \(\angle EOD = 17^{\circ}\) (measure of arc \(ED\)) and \(\angle DOC=90^{\circ}\) (right - angle), the measure of arc \(EDC\) is \(m\widehat{EDC}=m\widehat{ED}+m\widehat{DC}=17^{\circ}+90^{\circ} = 107^{\circ}\).

Step3: Calculate the measure of \(\widehat{EFC}\)

Using the formula \(m\widehat{EFC}=360^{\circ}-m\widehat{EDC}\). Substitute \(m\widehat{EDC} = 107^{\circ}\) into the formula: \(m\widehat{EFC}=360^{\circ}-107^{\circ}=253^{\circ}\).

Answer:

\(253^{\circ}\)