Math Problem Statement

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

Solution

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

Key observations:

  • SUVX\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.
  • UTR\angle UTR is an exterior angle with respect to the parallel lines and the transversal.
  • VWY\angle VWY is an alternate interior angle with UTR\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: mVWY=mUTR=123.8m\angle VWY = m\angle UTR = 123.8^\circ

Therefore, mVWY=123.8m\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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Parallel Lines
Transversals
Alternate Interior Angles

Formulas

Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, each pair of alternate interior angles are congruent.

Theorems

Alternate Interior Angles Theorem

Suitable Grade Level

Grades 8-10