1. **State the problem:** We are given two angles formed by intersecting lines: one angle is 62° and the opposite angle is labeled as $(x - 2)^\circ$. We need to find the value of $x$. 2. **Formula and rule:** When two lines intersect, opposite (vertical) angles are equal. This means: $$62 = x - 2$$ 3. **Solve the equation:** Add 2 to both sides: $$62 + 2 = x - 2 + 2$$ $$64 = x$$ 4. **Final answer:** $$x = 64$$ This means the value of $x$ that makes the angles equal is 64.