Question

1. find all the missing angles.

Explanation:

Step1: Vertical angles

Vertical angles are equal. So, $\angle 6 = 83^{\circ}$, $\angle 7=180^{\circ}-83^{\circ}=97^{\circ}$, $\angle 8 = 83^{\circ}$.

Step2: Corresponding angles

Since the lines are parallel, $\angle 2=\angle 6 = 83^{\circ}$, $\angle 4=\angle 8 = 83^{\circ}$.

Step3: Supplementary angles

$\angle 1 = 180^{\circ}-\angle 2=180^{\circ}-83^{\circ}=97^{\circ}$, $\angle 3=\angle 1 = 97^{\circ}$.

Answer:

$\angle 1 = 97^{\circ}$, $\angle 2 = 83^{\circ}$, $\angle 3 = 97^{\circ}$, $\angle 4 = 83^{\circ}$, $\angle 6 = 83^{\circ}$, $\angle 7 = 97^{\circ}$, $\angle 8 = 83^{\circ}$