1. **Problem Statement:** Given two parallel lines $O$ and $m$ cut by a transversal $k$, find the values of angles $z$ and $x$ where the angles are $(3x + 15)^\circ$, $z^\circ$, and $69^\circ$ as shown. 2. **Key Concept:** When two parallel lines are cut by a transversal, alternate interior angles are equal, and corresponding angles are equal. 3. **Identify Angles:** - The angle $(3x + 15)^\circ$ and $z^\circ$ are alternate interior angles, so they are equal: $$z = 3x + 15$$ - The angle $z^\circ$ and $69^\circ$ are corresponding angles on the other side of the transversal, so they are equal: $$z = 69$$ 4. **Find $x$:** Substitute $z = 69$ into $z = 3x + 15$: $$69 = 3x + 15$$ Subtract 15 from both sides: $$69 - 15 = 3x$$ $$54 = 3x$$ Divide both sides by 3: $$x = \frac{54}{3} = 18$$ 5. **Final Answers:** $$z = 69$$ $$x = 18$$