1. **State the problem:** We need to find the angle $x$ such that $\cos x = 2$. 2. **Recall the range of cosine:** The cosine function outputs values only in the range $[-1, 1]$ for all real numbers $x$. 3. **Analyze the given equation:** Since $2$ is outside the range $[-1, 1]$, there is no real angle $x$ for which $\cos x = 2$. 4. **Conclusion:** The equation $\cos x = 2$ has no solution in the real numbers. If considering complex solutions, the problem becomes more advanced and involves inverse cosine of values outside the real range, but for typical real-valued angles, no solution exists.