Find x in the second circle.

Let's analyze the second circle. Here, the measure of arc \(MK\) is \(124^{\circ}\) and the measure of arc \(NK\) is \(180^{\circ}\). The measure of arc \(MN\) is \(360^{\circ} - 124^{\circ} - 180^{\circ} = 56^{\circ}\). The angle \(x\) is the inscribed angle \(\angle MNK\) subtended by the arc \(MK\). The inscribed angle is half the measure of the intercepted arc. Therefore, $$x = \frac{1}{2} \cdot 124^{\circ} = 62^{\circ}$$ Thus, the value of \(x\) is \(62^{\circ}\). Answer: 62