Let's break down the problem shown in the image into individual exercises. I will help you solve each one step by step.

For the first diagram (with the intersecting lines):

You are tasked with finding the measures of all eight angles, labeled from $\angle 1$ to $\angle 8$, given the following information:

1. $m\angle 2 = 91^\circ$
2. $m\angle 3 = 75^\circ$
3. $m\angle 8 = x$

Step-by-Step Process:

1. If $m\angle 2 = 91^\circ$:

   • $\angle 2$ and $\angle 7$ are vertically opposite angles, so $m\angle 7 = 91^\circ$.
   • $\angle 2$ and $\angle 3$ are supplementary angles because they form a straight line. Therefore: $m\angle 3 + m\angle 2 = 180^\circ$ Since $m\angle 2 = 91^\circ$, we get: $m\angle 3 = 180^\circ - 91^\circ = 89^\circ$
   • Vertically opposite angles $\angle 1$ and $\angle 2$ are also equal, so $m\angle 1 = 89^\circ$.

2. If $m\angle 3 = 75^\circ$:

   • $\angle 3$ and $\angle 6$ are vertically opposite angles, so $m\angle 6 = 75^\circ$.
   • $\angle 3$ and $\angle 2$ are supplementary, but since $m\angle 2$ has already been determined as 91° (not 105°), we cannot use the information to revise this measure directly.