Question

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

Explanation:

Step1: Recall circle - arc property

The measure of a full - circle is 360°.

Step2: Identify known arcs

Since \(AE\) and \(FC\) are diameters, arc \(EFC\) and arc \(EDC\) together make up the full - circle. Arc \(EDC\) is composed of arc \(ED\) and arc \(DC\). The angle between \(FC\) and \(AE\) is 90°, so arc \(DC = 90^{\circ}\), and arc \(ED=17^{\circ}\). Then arc \(EDC=90^{\circ}+17^{\circ}=107^{\circ}\).

Step3: Calculate arc \(EFC\)

Let the measure of arc \(EFC\) be \(x\). We know that \(x + 107^{\circ}=360^{\circ}\). So \(x = 360^{\circ}-107^{\circ}=253^{\circ}\).

Answer:

253°