1. **Problem statement:** We have an isosceles triangle with two equal sides of length 8 cm and an included angle of 55° between them. We need to find the angle $x$ at the top vertex opposite the 55° angle. 2. **Formula used:** In any triangle, the sum of interior angles is 180°. For an isosceles triangle with two equal sides, the angles opposite those sides are equal. Let the two equal angles be $x$. 3. **Set up the equation:** $$55^\circ + x + x = 180^\circ$$ 4. **Simplify:** $$55^\circ + 2x = 180^\circ$$ 5. **Isolate $x$:** $$2x = 180^\circ - 55^\circ$$ $$2x = 125^\circ$$ 6. **Divide both sides by 2:** $$x = \frac{125^\circ}{2}$$ $$x = \cancel{\frac{125^\circ}{\cancel{2}}}$$ 7. **Final answer:** $$x = 62.5^\circ$$ Since 62.5° is closest to 60° among the options, the best choice is 60°. **Answer:** $x = 62.5^\circ$ (approximately 60°)