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Let's go over the problems in the image you uploaded.

### Problems 27 and 28:
These are asking about scenarios involving parallel lines and transversals.

- **Problem 27**: "Two parallel lines are intersected by a transversal so that the corresponding angles are supplementary."

    This situation is **impossible**. 
    - By definition, corresponding angles formed by a transversal with parallel lines are always **congruent** (i.e., equal). For them to be supplementary, they would have to sum to 180°, which can only happen if one angle was acute and the other obtuse. This would imply the lines are not parallel, making the scenario contradictory.

- **Problem 28**: "Two parallel lines are intersected by a transversal so that the same-side interior angles are complementary."

    This is also **impossible**. 
    - Same-side interior angles formed by a transversal with parallel lines are **supplementary** (i.e., their sum is 180°). For them to be complementary, they would need to sum to 90°, which is inconsistent with the properties of parallel lines.

### Problem 29:
This question involves a diagram with a transversal intersecting two parallel lines, and it gives angle measures.

- **Part (a)**: "What type of angle pair is ∠QRT and ∠STR?"

    These angles are **alternate interior angles** because they are on opposite sides of the transversal \( \overline{RT} \), between the parallel lines \( \overline{PS} \) and \( \overline{QR} \). By the **Alternate Interior Angle Theorem**, alternate interior angles are congruent.

- **Part (b)**: "Find \( m∠STR \)."

    Since \( \overline{RT} \) is a transversal and the angles are alternate interior angles, we can conclude that \( m∠STR = m∠QRT = 25^\circ \), by the theorem mentioned above.

Would you like further clarification on any of these solutions? Here are some related questions to practice:

1. How can we prove that corresponding angles are congruent when a transversal intersects parallel lines?
2. What is the difference between supplementary and complementary angles in terms of parallel lines and transversals?
3. How do we classify angles when the transversal is not perpendicular to the parallel lines?
4. Can two alternate exterior angles be supplementary?
5. What happens to angle measures when the lines are not parallel?

**Tip**: When working with parallel lines and transversals, always remember that corresponding, alternate interior, and alternate exterior angles are congruent, while same-side interior angles are supplementary!

Draw the given situation or tell why it is impossible: Two parallel lines are intersected by a transversal so that the corresponding angles are supplementary; Two parallel lines are intersected by a transversal so that the same-side interior angles are complementary. In the diagram, which represents the side view of a mystery spot, m∠SRT = 25°. RT is a transversal to PS and QR. What type of angle pair is ∠QRT and ∠STR? Find m∠STR.

Explore how to work with parallel lines intersected by a transversal and understand why corresponding angles cannot be supplementary, and same-side interior angles cannot be complementary. Learn about alternate interior angles and their properties with a detailed explanation of angles in a transversal.

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