Question: More Practice 1.6 Name Miranda Flores 1. Classify $\angle x$ and $\angle y$: __________ Classify $\angle y$ and $\angle z$: __________ 2. $m\angle x = ________$ $m\angle y = ________$ $118^\circ$ $79^\circ$ Graph shapes and math: Top-left: a right-angle marker at the intersection of a vertical ray and a horizontal ray, with an additional diagonal ray forming adjacent angles labeled $x$, $y$, and $z$. Top-right: two intersecting lines, one nearly horizontal and one diagonal, with the upper-left angle marked $118^\circ$ and adjacent angles labeled $x$ and $y$. Bottom-right: two rays forming a V-shape with the angle between them marked $79^\circ$, and a small slanted line extending left from the vertex.

1. **State the problem:** We need to classify the pairs of angles $\angle x$ and $\angle y$, and $\angle y$ and $\angle z$ from the given diagrams. Also, find the measures $m\angle x$ and $m\angle y$ given some angle measures. --- 2. **Classify $\angle x$ and $\angle y$ (Top-left diagram):** - The diagram shows a right angle (90°) formed by vertical and horizontal rays. - A diagonal ray creates three adjacent angles: $\angle x$, $\angle y$, and $\angle z$. - Since the right angle is 90°, and the three angles $x$, $y$, and $z$ are adjacent and sum to 90°: $$m\angle x + m\angle y + m\angle z = 90^\circ$$ - $\angle x$ and $\angle y$ share a common side and vertex, and are adjacent angles. - Therefore, $\angle x$ and $\angle y$ are **adjacent angles**. --- 3. **Classify $\angle y$ and $\angle z$ (Top-left diagram):** - Similarly, $\angle y$ and $\angle z$ are adjacent angles because they share a common side and vertex. - So, $\angle y$ and $\angle z$ are **adjacent angles**. --- 4. **Find $m\angle x$ and $m\angle y$ (Top-right diagram):** - The diagram shows two intersecting lines with an angle marked $118^\circ$ and adjacent angles $x$ and $y$. - Since the lines intersect, vertical angles are equal. - The angle adjacent to $118^\circ$ and labeled $x$ forms a linear pair with $118^\circ$. - Linear pairs sum to $180^\circ$: $$m\angle x + 118^\circ = 180^\circ$$ - Solve for $m\angle x$: $$m\angle x = 180^\circ - 118^\circ = 62^\circ$$ - $\angle x$ and $\angle y$ are vertical angles, so: $$m\angle y = m\angle x = 62^\circ$$ --- 5. **Summary:** - $\angle x$ and $\angle y$ are adjacent angles (top-left). - $\angle y$ and $\angle z$ are adjacent angles (top-left). - $m\angle x = 62^\circ$ (top-right). - $m\angle y = 62^\circ$ (top-right).