1. **Stating the problem:** We are given two intersecting lines at point O forming vertical angles. One angle, $\angle POR$, is given as 146°. 2. **Understanding vertical angles:** Vertical angles are the angles opposite each other when two lines intersect. They are always equal. 3. **Finding $\angle POR$:** Since $\angle POR$ is given as 146°, we have $\angle POR = 146^\circ$. 4. **Finding $\angle ROQ$:** $\angle ROQ$ is adjacent to $\angle POR$ on the straight line $POQ$. Angles on a straight line sum to 180°. 5. **Calculate $\angle ROQ$:** $$\angle ROQ = 180^\circ - \angle POR = 180^\circ - 146^\circ = 34^\circ$$ **Final answers:** $\angle POR = 146^\circ$, $\angle ROQ = 34^\circ$