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The diagram shows two parallel lines, \( m \) and \( n \), with transversals \( s \) and \( t \) intersecting them at point \( P \). The angles formed at point \( P \) include a 30° angle above line \( m \) and a 70° angle below line \( n \). The angle marked \( x \) is also shown at point \( P \).

### Solution:
Given:
- \( m \parallel n \)
- \( \angle Psm = 30^\circ \)
- \( \angle Ptn = 70^\circ \)

Since \( m \) and \( n \) are parallel lines and \( s \) and \( t \) are transversals, the corresponding angles are equal.

Thus, \( \angle Psm = \angle sP \) (corresponding angles),
which gives \( \angle sP = 30^\circ \).

Similarly, since \( t \) is a transversal, \( \angle tP \) is corresponding to \( \angle Ptn = 70^\circ \).

We also know that the sum of angles around point \( P \) on a straight line equals 180°.

\[ \angle sP + x + \angle tP = 180^\circ \]

Substitute the known values:

\[ 30^\circ + x + 70^\circ = 180^\circ \]

\[ 100^\circ + x = 180^\circ \]

Solving for \( x \):

\[ x = 180^\circ - 100^\circ \]
\[ x = 80^\circ \]

### Final Answer:
The value of \( x \) is \( 80^\circ \).

Would you like more details or have any further questions?

### Follow-Up Questions:
1. What are corresponding angles, and why are they equal in this scenario?
2. Can you explain how the sum of angles on a straight line equals 180°?
3. How would the solution change if the given angles were different?
4. What is the relationship between alternate interior angles when lines are parallel?
5. How would you solve for \( x \) if the lines \( m \) and \( n \) were not parallel?

### Tip:
When dealing with parallel lines and a transversal, always remember that corresponding angles are equal, and the sum of angles on a straight line is 180°.

Explore how to solve angle problems involving parallel lines and transversals. This example problem demonstrates the use of corresponding angles and the sum of angles on a straight line theorem. Suitable for Grades 7-9 students learning geometry.

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