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

In circle O, and are diameters. Arc ED measures 17°. What is the measure of? 107° 180° 253° 270°

Answer: The correct answer is Arc EFC = 253°.

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°

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