1. The problem states that we have two intersecting lines forming vertical angles. 2. Vertical angles are always equal. 3. Given one angle is $62^\circ$, the angle opposite to it, labeled $t$, must be equal to $62^\circ$. 4. Therefore, the value of $t$ is: $$t = 62^\circ$$ This is because vertical angles are congruent (equal in measure).