1. **Problem Statement:** Given a diagram with two parallel lines cut by a transversal, find the unknown angles $x$, $y$, and $z$ using properties of corresponding angles, interior angles, alternate interior angles, and vertically opposite angles. 2. **Key Formulas and Rules:** - Corresponding angles are equal. - Alternate interior angles are equal. - Interior angles on the same side of the transversal are supplementary, i.e., their sum is $180^\circ$. - Vertically opposite angles are equal. 3. **Example Setup:** Suppose two parallel lines $l_1$ and $l_2$ are cut by a transversal $t$. Given angles: one angle is $50^\circ$, another is $z$, and we need to find $x$ and $y$. 4. **Step-by-step Solution:** - Since corresponding angles are equal, if one angle is $50^\circ$, the corresponding angle $x$ is also $50^\circ$. - Alternate interior angles are equal, so $y = 50^\circ$. - Interior angles on the same side of the transversal add up to $180^\circ$, so $z + 50 = 180$. - Solve for $z$: $$z = 180 - 50 = 130^\circ$$. 5. **Summary:** - $x = 50^\circ$ - $y = 50^\circ$ - $z = 130^\circ$ This worksheet helps practice identifying and calculating unknown angles using the properties of parallel lines and a transversal.