Let's analyze the image to determine the measures of angles 6, 7, and 8.

1. Given Information:

   • Angle 1 is $22^\circ$.
   • Angle 2 is $90^\circ$ (since there is a right angle mark at that point).
   • Lines $a$ and $b$ are parallel.
   • Line $t$ is a transversal that cuts lines $a$ and $b$.

2. Find Angle 6: Angle 6 is an alternate interior angle to angle 1 (since they are on opposite sides of the transversal and between two parallel lines). Therefore: $\text{Angle 6} = 22^\circ$

3. Find Angle 7: Angle 7 and angle 6 form a linear pair (i.e., they are on the same line and add up to $180^\circ$). So: $\text{Angle 7} = 180^\circ - 22^\circ = 158^\circ$

4. Find Angle 8: Angle 8 is a corresponding angle to angle 2. Corresponding angles are equal, so: $\text{Angle 8} = 90^\circ$

Summary of the Measures:

• Angle 6: $22^\circ$
• Angle 7: $158^\circ$
• Angle 8: $90^\circ$

Let me know if you'd like further details or have any questions!

Here are some relative questions for deeper understanding:

1. What is the relationship between alternate interior angles and parallel lines?
2. How do corresponding angles help in finding unknown angles?
3. Can linear pairs always be used to find angles?
4. How does a transversal affect angle measures between parallel lines?
5. What are other methods for solving unknown angles in a geometric figure?

Tip: When working with parallel lines and a transversal, always look for alternate interior, corresponding, or consecutive interior angles to solve for unknown angles.