Question

1. use the given angle to find the remaining angle measures in the diagram.

Explanation:

Step1: Vertical - angle property

Vertical angles are equal. $\angle5$ and the $50^{\circ}$ angle are vertical angles, so $m\angle5 = 50^{\circ}$. Also, $\angle7$ and the $50^{\circ}$ angle are vertical angles, so $m\angle7=50^{\circ}$.

Step2: Supplementary - angle property

$\angle5$ and $\angle8$ are supplementary (linear - pair), so $m\angle8 = 180^{\circ}-m\angle5=180 - 50=130^{\circ}$. Similarly, $\angle7$ and $\angle6$ are supplementary, so $m\angle6 = 130^{\circ}$.

Step3: Corresponding - angle property

Corresponding angles are equal. $\angle1$ and $\angle5$ are corresponding angles, so $m\angle1 = 50^{\circ}$. $\angle2$ and $\angle6$ are corresponding angles, so $m\angle2 = 130^{\circ}$. $\angle3$ and $\angle7$ are corresponding angles, so $m\angle3 = 50^{\circ}$. $\angle4$ and $\angle8$ are corresponding angles, so $m\angle4 = 130^{\circ}$.

Answer:

$m\angle1 = 50^{\circ}$, $m\angle2 = 130^{\circ}$, $m\angle3 = 50^{\circ}$, $m\angle4 = 130^{\circ}$, $m\angle5 = 50^{\circ}$, $m\angle6 = 130^{\circ}$, $m\angle7 = 50^{\circ}$, $m\angle8 = 130^{\circ}$