1. The problem is to find the value of $\tan 135^\circ$. 2. Recall the tangent function and its properties: $\tan(\theta) = \frac{\sin \theta}{\cos \theta}$. 3. Note that $135^\circ$ is in the second quadrant where sine is positive and cosine is negative. 4. Use the angle subtraction identity: $135^\circ = 180^\circ - 45^\circ$. 5. Since $\tan(180^\circ - \theta) = -\tan \theta$, we have: $$\tan 135^\circ = -\tan 45^\circ$$ 6. We know $\tan 45^\circ = 1$, so: $$\tan 135^\circ = -1$$ Final answer: $\boxed{-1}$