Question

complete the proof that ( mangle qrw + mangle put = 180^{circ} ).

Explanation:

Step1: Recall the definition of same - side interior angles

When two parallel lines are cut by a transversal, same - side interior angles are supplementary.
Since \( \overleftrightarrow{EG}\parallel\overleftrightarrow{TV}\) and \( \overleftrightarrow{WP}\) is a transversal.

Step2: Identify the relationship between \( \angle EFW\) and \( \angle PUT\)

\( \angle EFW\) and \( \angle PUT\) are same - side interior angles.
By the Same - Side Interior Angles Theorem, \(m\angle EFW + m\angle PUT=180^{\circ}\)

Answer:

Same - Side Interior Angles Theorem