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In the given image, you have triangle \( \triangle TUV \), and the line \( WTX \) is drawn such that \( WTX \parallel UV \).

From the diagram, we are given two angles:
- \( \angle TUV = 82^\circ \)
- \( \angle TUX = 53^\circ \)

We need to determine \( m\angle TUV \).

Since the line \( WTX \parallel UV \), this forms a pair of corresponding angles between the transversal \( TU \). Therefore, \( \angle TWX = \angle TUV \) by the Corresponding Angles Postulate. This means that \( \angle TWX = 82^\circ \).

Thus, \( m\angle TUV = 82^\circ \).

Do you want any further details or clarification?

### Here are some related questions for further practice:
1. How do you find corresponding angles when parallel lines are involved?
2. What is the sum of the interior angles of a triangle?
3. How can you verify that two lines are parallel based on angle relationships?
4. What other angle properties can you use when parallel lines and transversals are present?
5. Can the exterior angle theorem be applied to solve any angles here?

### Tip: 
Remember, when two lines are parallel, corresponding angles are always equal when cut by a transversal. This property is highly useful in geometry problems involving parallel lines.

In the figure below, △TUV is drawn. The line WTX is drawn such that WTX is parallel to UV. The angles in the triangle include ∠TUV = 82° and ∠TUX = 53°. What is the measure of ∠TUV?

Learn how to find the measure of ∠TUV in △TUV where a line WTX is parallel to UV. This problem uses the Corresponding Angles Postulate and geometry concepts related to triangles. Suitable for students in Grade 9-10.

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