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The problem asks to find the measure of \( \angle 10 \) using the properties of parallel lines and a transversal. Here's how we can approach it:

### Given:
1. Lines \( a \) and \( b \) are parallel and cut by a transversal \( t \).
2. \( \angle 7 = 94^\circ \).
3. \( \angle 7 \) and \( \angle 8 \) are consecutive interior angles.
4. \( \angle 8 \) and \( \angle 10 \) are alternate interior angles.

### Steps:

1. **Consecutive Interior Angles:**
   - Since \( \angle 7 \) and \( \angle 8 \) are consecutive interior angles and the lines are parallel, they are supplementary. This means:
     \[
     \angle 7 + \angle 8 = 180^\circ
     \]
     Substituting the value of \( \angle 7 \):
     \[
     94^\circ + \angle 8 = 180^\circ
     \]
     \[
     \angle 8 = 180^\circ - 94^\circ = 86^\circ
     \]

2. **Alternate Interior Angles:**
   - \( \angle 8 \) and \( \angle 10 \) are alternate interior angles, and because lines \( a \) and \( b \) are parallel, alternate interior angles are congruent. Therefore:
     \[
     \angle 10 = \angle 8 = 86^\circ
     \]

### Final Answer:
\[
\boxed{86^\circ}
\]

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. What is the relationship between alternate interior angles when two lines are parallel?
2. How are consecutive interior angles related to each other when two lines are parallel?
3. Can you find the measure of \( \angle 9 \) in the same scenario?
4. What would happen if the lines were not parallel? How would this affect the angle measures?
5. How do corresponding angles relate to alternate interior angles?

**Tip:** Always remember that parallel lines with a transversal create congruent alternate interior and corresponding angles.

Lines a and b are parallel and are cut by transversal t to form interior angles 7, 8, 9, and 10. Angle 7 and Angle 8 are consecutive interior angles, and Angle 7 = 94°. Angle 8 and Angle 10 are alternate interior angles. Find the measure of Angle 10.

This problem involves parallel lines cut by a transversal, forming consecutive and alternate interior angles. Using the fact that Angle 7 is 94°, we can find Angle 10 by applying the properties of consecutive and alternate interior angles. Suitable for students in Grades 7-10.

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