Question

In circle O, and are diameters. Arc ED measures 17°. Circle O is shown. Line segments F C and A E are diameters. Line segments C O and B O are radii. Point B is between points A and C, and point C is between points E and C. Angle D C is a right angle. What is the measure of Arc E F C? 107° 180° 253° 270°

Answer 1

253

Explanation:

Answer 2

Arc EFC = 253°

Explanation:

Figure attached.

We know there are 360 degrees in a circle.

Looking at the figure, we can say:

Arc EFC + Arc CD + Arc DE = 360

Arc CD is 90 degrees since the central angle is 90 degrees given [the central angle of an intercepted arc is equal to the measure of the arc].

Arc DE (aka arc ED) is given as 17 degrees

Now we plug them into the equation and solve:

Arc EFC + Arc CD + Arc DE = 360

Arc EFC + 90 + 17 = 360

Arc EFC + 107 = 360

Arc EFC = 360 - 107

Arc EFC = 253

Thus, Arc EFC = 253°