Math Problem Statement

Which angles are vertical angles?

Solution

In the provided diagram, you are asked to identify the pair of vertical angles. Vertical angles are formed when two lines intersect, and they are opposite angles that are equal to each other.

Looking at the diagram:

  • Lines MOMO and PRPR are parallel, and line LNLN acts as a transversal. Also, line PQPQ intersects PRPR at point QQ, creating additional intersections.

Now, analyzing angle pairs:

  • PQS\angle PQS is formed at point QQ between lines PQPQ and RSRS.
  • The angle directly opposite PQS\angle PQS would be MNQ\angle MNQ, which forms at the same intersection but on the opposite side of point QQ.

Therefore, the pair of vertical angles is: PQS and MNQ\angle PQS \text{ and } \angle MNQ

The correct answer is: PQS\angle PQS and MNQ\angle MNQ.

Would you like further details on how vertical angles are identified?

Here are some related questions:

  1. What are the properties of vertical angles?
  2. How are parallel lines used to find corresponding angles?
  3. How does a transversal line affect the angles in parallel lines?
  4. What are alternate interior angles?
  5. What is the difference between adjacent and vertical angles?

Tip: Vertical angles are always equal, and they are formed by the intersection of two lines, appearing directly opposite each other.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Parallel Lines
Transversal Lines
Vertical Angles
Intersecting Lines

Formulas

-

Theorems

Vertical Angles Theorem

Suitable Grade Level

Grades 8-10