Question

find the measures of angles x, y, and z in the figure. ∠y = 139° ∠x =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle $y$ and the given $139^{\circ}$ angle are vertical angles, so $y = 139^{\circ}$. Angle $x$ and the given $139^{\circ}$ angle are supplementary (they form a straight - line pair).

Step2: Calculate angle $x$

The sum of supplementary angles is $180^{\circ}$. So $x=180 - 139$.
$x = 41^{\circ}$

Step3: Calculate angle $z$

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

Answer:

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