what is the measure of ced? 106° 108° 148° 212°

Answer

Explanation:

Step1: Recall circle - arc relationship

The sum of the measures of the arcs of a circle is 360°.

Step2: Identify known arcs

We know that one arc $\overset{\frown}{CD}$ has a central - angle measure of 160° and another arc $\overset{\frown}{CE}$ has a central - angle measure of 52°.

Step3: Calculate $\overset{\frown}{CED}$

$\overset{\frown}{CED}=\overset{\frown}{CD}+\overset{\frown}{DE}$. First, find the measure of $\overset{\frown}{DE}$. The sum of the central angles of the arcs in a circle is 360°. Let the measure of $\overset{\frown}{DE}=x$. Then $160 + 52+x=360$. Solving for $x$, we get $x = 360-(160 + 52)=148$. And $\overset{\frown}{CED}=\overset{\frown}{CE}+\overset{\frown}{DE}=52 + 148=212^{\circ}$.

Answer:

212°