The problem asks to find the value of $x$ in a circle where the arc $JK$ has a measure of $23$ degrees, the arc $KL$ has a measure of $x$ degrees, and the arc $JL$ has a measure of $96$ degrees.

1. Problem Description

The problem asks to find the value of $x$ in a circle where the arc $JK$ has a measure of $23$ degrees, the arc $KL$ has a measure of $x$ degrees, and the arc $JL$ has a measure of $96$ degrees.

2. Solution Steps

The measure of an arc is equal to the measure of the central angle that subtends it. Since $JK = 23$ and $KL = x$, then $JL = JK + KL$.

Thus, $96 = 23 + x$.

Subtracting $23$ from both sides gives $x = 96 - 23$.

Therefore, $x = 73$.

3. Final Answer

$x = 73$