Question

3 - geometry question 9, 6.1.39 part 1 of 3 hw score: 31.03%, 18 of 58 points points: 0 of 1 find the measures of angles x, y, and z in the figure.

Explanation:

Step1: Use vertical - angles property

Vertical angles are equal. Angle $x$ and the $139^{\circ}$ angle are vertical angles, so $x = 139^{\circ}$.

Step2: Use linear - pair property

Angles $x$ and $y$ form a linear pair. The sum of angles in a linear pair is $180^{\circ}$. So $y=180 - x$. Substituting $x = 139^{\circ}$, we get $y = 180-139=41^{\circ}$.

Step3: Use vertical - angles property again

Angle $y$ and angle $z$ are vertical angles. Since vertical angles are equal, $z = y=41^{\circ}$.

Answer:

$x = 139^{\circ}$, $y = 41^{\circ}$, $z = 41^{\circ}$