Question

complete the proof that ( mangle qvw + mangle tsx = 180^{circ} ).

Explanation:

Step1: Identify parallel lines and transversal

Since \( \overleftrightarrow{IK}\parallel\overleftrightarrow{UW}\) (given in step 2) and \(QX\) is a transversal.

Step2: Apply the Alternate Interior Angles Theorem

When two parallel lines (\( \overleftrightarrow{IK}\) and \( \overleftrightarrow{UW}\)) are cut by a transversal (\(QX\)), alternate - interior angles are congruent. So, \( \angle QVW\cong\angle KJQ\) by the Alternate Interior Angles Theorem.

Answer:

Alternate Interior Angles Theorem.