1. **State the problem:** We have an isosceles triangle with one angle given as 104° and the two base angles equal, one labeled as $92 - 2x$ degrees. We need to find the value of $x$. 2. **Recall the properties of an isosceles triangle:** The two base angles are equal. The sum of all angles in any triangle is 180°. 3. **Set up the equation:** Let the two equal base angles be $92 - 2x$ each. The top angle is 104°. So, $$104 + (92 - 2x) + (92 - 2x) = 180$$ 4. **Simplify the equation:** $$104 + 92 - 2x + 92 - 2x = 180$$ $$104 + 184 - 4x = 180$$ $$288 - 4x = 180$$ 5. **Solve for $x$:** $$-4x = 180 - 288$$ $$-4x = -108$$ $$x = \frac{-108}{-4} = 27$$ 6. **Final answer:** $$\boxed{27}$$