Answer
The central angle will be one-half of the original measurement (or halved).
Work Step by Step
Recall:
The arclength of a circle is given by the formula $S=r\theta$ where $r$=radius of the circle and $\theta$=the measure of the central angle.
Deriving the formula for the central angle gives:
\begin{align*}
S&=r\theta\\\\
\frac{S}{r}&=\frac{r\theta}{r}\\\\
\frac{S}{r}&=\theta\\\\
\theta&=\frac{S}{r}
\end{align*}
Suppose the length of a certain arc is $5$.
Substituting $5$ to $S$ in the formula above gives $\theta=\dfrac{5}{2r}$.
If the radius is doubled and the arclength $S$ is retained, then the central angle becomes:
$$\theta=\dfrac{5}{2r}$$
Notice that the central angle $\theta$ was reduced to $\dfrac{1}{2}$ of the original measurement.
Therefore, when the radius of a circle is doubled (with everything else unchanged), the central angle measurement will be $\bf\text{halved}$.
