Question

given line a || line b, line c || line d. drag and drop the angle measures.

Explanation:

Step1: Identify vertical - angle relationship

$\angle1$ and the $134^{\circ}$ angle are vertical angles. Since vertical angles are equal, $\angle1 = 134^{\circ}$.

Step2: Use linear - pair relationship

$\angle1$ and $\angle2$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So, $\angle2=180 - 134=46^{\circ}$.

Step3: Use corresponding - angle relationship

Since $a\parallel b$ and $c\parallel d$, $\angle2$ and $\angle4$ are corresponding angles, so $\angle4 = 46^{\circ}$. Also, $\angle1$ and $\angle6$ are corresponding angles, so $\angle6 = 134^{\circ}$. And $\angle2$ and $\angle5$ are corresponding angles, so $\angle5 = 46^{\circ}$. $\angle1$ and $\angle3$ are vertical angles, so $\angle3 = 134^{\circ}$.

Answer:

$\angle1 = 134^{\circ}$, $\angle2 = 46^{\circ}$, $\angle3 = 134^{\circ}$, $\angle4 = 46^{\circ}$, $\angle5 = 46^{\circ}$, $\angle6 = 134^{\circ}$