Question

1 determine each unknown measure in the figure. explain your reasoning.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Since $x$ and $122^{\circ}$ are vertical angles, $x = 122^{\circ}$.

Step2: Use linear - pair property

The sum of angles in a linear pair is $180^{\circ}$. Since $x$ and $y$ form a linear pair, $x + y=180^{\circ}$. Substituting $x = 122^{\circ}$, we get $y=180 - 122=58^{\circ}$.

Step3: Use vertical - angle property again

Since $y$ and $z$ are vertical angles, $z = y$. So $z = 58^{\circ}$.

Answer:

$x = 122^{\circ}$, $y = 58^{\circ}$, $z = 58^{\circ}$