1. **Stating the problem:** We are given a diagram with two intersecting lines forming angles labeled 60°, 110°, 51°, and 22°. We need to find the unknown angles $\angle v$, $\angle x$, $\angle y$, and $\angle w$ inside the intersection area. 2. **Important rules:** - Vertical angles are equal. - Adjacent angles on a straight line sum to 180°. 3. **Find $\angle v$:** Since $\angle v$ is vertical to the 110° angle, by the vertical angle theorem: $$\angle v = 110^\circ$$ 4. **Find $\angle x$:** $\angle x$ and 60° are adjacent angles on a straight line, so: $$\angle x + 60^\circ = 180^\circ$$ $$\angle x = 180^\circ - 60^\circ = 120^\circ$$ 5. **Find $\angle y$:** $\angle y$ is vertical to 51°, so: $$\angle y = 51^\circ$$ 6. **Find $\angle w$:** $\angle w$ and 22° are adjacent on a straight line, so: $$\angle w + 22^\circ = 180^\circ$$ $$\angle w = 180^\circ - 22^\circ = 158^\circ$$ **Final answers:** $$\angle v = 110^\circ, \quad \angle x = 120^\circ, \quad \angle y = 51^\circ, \quad \angle w = 158^\circ$$