1. **State the problem:** We have a triangle with interior angles 64° and 27°, and an exterior angle at the left vertex labeled as $97 + x$. We need to find the value of $x$. 2. **Recall the exterior angle theorem:** The exterior angle of a triangle is equal to the sum of the two opposite interior angles. 3. **Set up the equation:** $$97 + x = 64 + 27$$ 4. **Simplify the right side:** $$97 + x = 91$$ 5. **Isolate $x$ by subtracting 97 from both sides:** $$\cancel{97} + x = 91 - \cancel{97}$$ $$x = -6$$ 6. **Interpretation:** The value of $x$ is $-6$. **Final answer:** $x = -6$