1. We are given a triangle with one angle of 15° and another angle of 45°, and an unknown angle $x$ adjacent to the 15° angle. 2. In a triangle, the sum of interior angles is always 180°. 3. Let the third angle be $x$. Then we have the equation: $$15^\circ + 45^\circ + x = 180^\circ$$ 4. Simplify the sum of the known angles: $$60^\circ + x = 180^\circ$$ 5. Subtract 60° from both sides to solve for $x$: $$x = 180^\circ - 60^\circ = 120^\circ$$ 6. The problem also mentions that the sides opposite the 15° and 45° angles are equal, which indicates this is an isosceles triangle. 7. Since the triangle has two sides equal, angles opposite those sides must be equal, but here the angles are not equal (15° and 45°), so the equality of opposite sides suggests a specific labeling or perhaps $x$ relates to another angle formed by these sides. 8. However, based solely on the given information and the angle sum property, $x$ is $120^\circ$. Final answer: $x = 120^\circ$