The problem states that the end of a charger plugged into a phone is an isosceles trapezoid. Given that the measure of angle $N$ is $140^{\circ}$, we need to find the measure of angle $K$.

1. Problem Description

The problem states that the end of a charger plugged into a phone is an isosceles trapezoid. Given that the measure of angle $N$ is $140^{\circ}$, we need to find the measure of angle $K$.

2. Solution Steps

In an isosceles trapezoid, the base angles are equal.

Therefore, $m\angle N = m\angle M = 140^{\circ}$.

Also, consecutive angles between the bases are supplementary, meaning they add up to $180^{\circ}$.

So, $m\angle K + m\angle M = 180^{\circ}$ and $m\angle J + m\angle N = 180^{\circ}$.

Substituting the value of $m\angle M$, we have $m\angle K + 140^{\circ} = 180^{\circ}$.

Solving for $m\angle K$, we get $m\angle K = 180^{\circ} - 140^{\circ} = 40^{\circ}$.

3. Final Answer

$m\angle K = 40^{\circ}$