https://file.aiquickdraw.com/mathbot/file/1728487730639xzt3j796.jpg

The diagram shows two parallel lines \( \overline{SU} \) and \( \overline{VX} \) that are intersected by a transversal \( \overline{WY} \). We are given that \( m\angle UTR = 123.8^\circ \), and the goal is to determine the measure of \( m\angle VWY \).

### Key observations:
- \( \overline{SU} \parallel \overline{VX} \) implies that angles formed by the transversal will have special relationships such as corresponding angles, alternate interior angles, and consecutive interior angles.
- \( \angle UTR \) is an exterior angle with respect to the parallel lines and the transversal.
- \( \angle VWY \) is an alternate interior angle with \( \angle UTR \), since they are on opposite sides of the transversal and between the two parallel lines.

### Relationship of angles:
For two parallel lines, alternate interior angles are congruent. Thus:
\[
m\angle VWY = m\angle UTR = 123.8^\circ
\]

Therefore, \( m\angle VWY = 123.8^\circ \).

Would you like further clarification or more details on how I approached this?

### 5 Related Questions:
1. What are alternate interior angles, and why are they congruent when lines are parallel?
2. Can you explain corresponding angles and how they relate to parallel lines?
3. How would the angles change if the lines were not parallel?
4. What are consecutive interior angles, and how do they differ from alternate interior angles?
5. How can we use the concept of vertical angles to solve similar problems?

### Tip:
When dealing with parallel lines and a transversal, always look for angle pairs like corresponding angles or alternate interior angles, as they provide a straightforward way to find missing angle measures.

If \( \overline{SU} \) and \( \overline{VX} \) are parallel lines and \( m\angle UTR = 123.8^\circ \), what is \( m\angle VWY \)?

Learn how to find the measure of angle \( m\angle VWY \) when two parallel lines are intersected by a transversal, and given \( m\angle UTR = 123.8^\circ \). This problem uses the Alternate Interior Angles Theorem and is suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation