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In the given figure, it is provided that the measure of angle \( \angle 7 = 100^\circ \). To find the measure of \( \angle 9 \), we can use the following reasoning based on the properties of parallel lines and transversals:

1. Lines \( m \), \( t \), and \( u \) appear to be parallel, and line \( s \) serves as a transversal.
2. \( \angle 7 \) and \( \angle 9 \) are **corresponding angles** because they are on the same side of the transversal \( s \) and on the same relative positions with respect to lines \( t \) and \( u \). 
3. For corresponding angles formed by a transversal crossing parallel lines, the angles are congruent, meaning their measures are equal.

Therefore, \( \angle 9 = \angle 7 = 100^\circ \).

### Answer:
\( \boxed{100^\circ} \)

Let me know if you'd like more details! Here are five related questions to explore:

1. What is the measure of \( \angle 5 \) in this figure?
2. How do you determine the relationship between alternate interior angles?
3. What is the measure of \( \angle 11 \) based on this diagram?
4. How do vertical angles relate in this configuration?
5. What is the total sum of angles formed at point \( t \) by the intersecting lines?

**Tip:** Remember that corresponding angles are always equal when a transversal cuts across parallel lines.

In the figure, m∠7 = 100°. Find the measure of ∠9.

In this problem, we use the concept of corresponding angles to find the measure of angle 9. Given m∠7 = 100°, learn how corresponding angles formed by a transversal cutting parallel lines are congruent. Suitable for students in Grades 8-10.

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