1. **State the problem:** We are given two intersecting lines forming vertical angles. One angle measures 152° and we need to find the measures of angles $x$, $y$, and $z$. 2. **Recall the properties of vertical angles:** Vertical angles are equal. Also, adjacent angles formed by intersecting lines are supplementary, meaning their measures add up to 180°. 3. **Identify the angles:** The given angle is 152°. Its vertical angle $x$ is equal to 152° because vertical angles are congruent. 4. **Find angle $y$:** Angle $y$ is adjacent to the 152° angle, so they are supplementary. $$y + 152 = 180$$ 5. **Solve for $y$:** $$y = 180 - 152 = 28$$ 6. **Find angle $z$:** Angle $z$ is vertical to angle $y$, so $z = y = 28$°. **Final answers:** $$x = 152^\circ, \quad y = 28^\circ, \quad z = 28^\circ$$