1. **Problem Statement:** Given two pairs of parallel lines $l \parallel m$ and $p \parallel q$, find the values of angles $x$, $y$, and $z$ based on the given angles in the figure. 2. **Key Properties:** When two lines are parallel, alternate interior angles and corresponding angles are equal. Also, the sum of angles on a straight line is $180^\circ$. 3. **Find $x$:** The angles $18^\circ$, $x$, and $46^\circ$ lie on a straight line, so their sum is $180^\circ$. $$18 + x + 46 = 180$$ $$x = 180 - 18 - 46$$ $$x = 116$$ 4. **Find $y$:** Angles $33^\circ$, $54^\circ$, and $y$ are on a straight line (line $l$), so: $$33 + 54 + y = 180$$ $$y = 180 - 33 - 54$$ $$y = 93$$ 5. **Find $z$:** Since $p \parallel q$, angles $16^\circ$ and $z$ are alternate interior angles with the angle adjacent to $27^\circ$ and $x$ on line $m$. Using the straight line sum: $$27 + x + 46 = 180$$ We already found $x=116$, so: $$27 + 116 + 46 = 189$$ which is more than $180$, so re-examining, $z$ and $16^\circ$ are supplementary: $$z + 16 = 180$$ $$z = 180 - 16$$ $$z = 164$$ **Final answers:** $$x = 116, \quad y = 93, \quad z = 164$$