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Circle B is shown. Line segments CB, DB, and EB are radii. Angle CBE is 52 degrees, and angle EBD is 160 degrees.

What is the measure of Arc CED?

A. 106°
B. 108°
C. 148°
D. 212°

Answer :

Final answer:

To find the measure of Arc CED, subtract the measure of angle CBE from a full circle to find the measure of Arc CBE. Subtract the measure of angle EBD from a full circle to find the measure of Arc BD. Add the measures of Arc CBE and Arc BD to find the measure of Arc CED, which is 508 degrees.

Explanation:

To find the measure of Arc CED, we can use the fact that the measure of an angle formed by two intersecting chords is equal to half the sum of the intercepted arcs. We can first find the measure of Arc CBE by subtracting the measure of angle CBE from a full circle, which is 360 degrees. In this case, Arc CBE would be 360 degrees minus 52 degrees, resulting in 308 degrees. Similarly, we can find the measure of Arc BD by subtracting the measure of angle EBD from a full circle. Arc BD would be 360 degrees minus 160 degrees, resulting in 200 degrees. Finally, we can find the measure of Arc CED by adding Arc CBE and Arc BD. Therefore, Arc CED would be 308 degrees plus 200 degrees, resulting in 508 degrees.

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