We need to find the measure of angle $MKL$. We are given the measure of angle $JKM$ is $92^\circ$ and the measure of angle $JKL$ is $148^\circ$.

1. Problem Description

We need to find the measure of angle $MKL$. We are given the measure of angle $JKM$ is $92^\circ$ and the measure of angle $JKL$ is $148^\circ$.

2. Solution Steps

We know that the measure of angle $JKL$ is the sum of the measures of angle $JKM$ and angle $MKL$. Therefore, we can write the following equation:

$m\angle JKL = m\angle JKM + m\angle MKL$

We are given $m\angle JKL = 148^\circ$ and $m\angle JKM = 92^\circ$.

Substituting these values into the equation, we get:

$148^\circ = 92^\circ + m\angle MKL$

To solve for $m\angle MKL$, we subtract $92^\circ$ from both sides of the equation:

$m\angle MKL = 148^\circ - 92^\circ$

$m\angle MKL = 56^\circ$

3. Final Answer

The measure of angle $MKL$ is $56^\circ$.

Final Answer: The final answer is $\boxed{56}$