Question

1. generalize in the diagram shown, if x + y = 180, label the remaining angles as x° or y°.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle vertical to the given $x^{\circ}$ angle is also $x^{\circ}$.

Step2: Use linear - pair property

Since $x + y=180$, and the angle adjacent to the given $x^{\circ}$ angle forms a linear - pair with it, that adjacent angle is $y^{\circ}$. Then, using vertical - angle property again, the angle vertical to this $y^{\circ}$ angle is also $y^{\circ}$.

Answer:

The angle vertical to the given $x^{\circ}$ is $x^{\circ}$, the angle adjacent to the given $x^{\circ}$ (forming a linear - pair) is $y^{\circ}$, and the angle vertical to this $y^{\circ}$ is $y^{\circ}$.