Question

do now the m∠6 = 82° find the measure of all the other numbered angles

Explanation:

Step1: Vertical - angle property

$\angle6$ and $\angle8$ are vertical angles, so $m\angle8 = 82^{\circ}$. $\angle6$ and $\angle4$ are corresponding angles, so $m\angle4=82^{\circ}$. $\angle4$ and $\angle2$ are vertical angles, so $m\angle2 = 82^{\circ}$.

Step2: Supplementary - angle property

$\angle6$ and $\angle5$ are supplementary. So $m\angle5=180 - 82=98^{\circ}$. $\angle5$ and $\angle7$ are vertical angles, so $m\angle7 = 98^{\circ}$. $\angle5$ and $\angle3$ are corresponding angles, so $m\angle3=98^{\circ}$. $\angle3$ and $\angle1$ are vertical angles, so $m\angle1 = 98^{\circ}$.

Answer:

$m\angle1 = 98^{\circ}$, $m\angle2 = 82^{\circ}$, $m\angle3 = 98^{\circ}$, $m\angle4 = 82^{\circ}$, $m\angle5 = 98^{\circ}$, $m\angle7 = 98^{\circ}$, $m\angle8 = 82^{\circ}$