Question

what is the missing statement for step 7?m∠sqv + m∠sqt = 180°m∠sqv + m∠vqt = m∠vqt + m∠zrsm∠vqt + m∠zrs = 180°m∠sqv + m∠vqt = 180°∠sqv ≅ ∠zrsm∠sqv = m∠zrsm∠sqv + m∠vqt - m∠vqt = m∠vqt + m∠zrs - m∠vqtdefinition of congruencysubtraction property of equalitysubstitution property of equalitysame - side interior angles theorem

Explanation:

Step1: Analyze the relationship between angles

In geometry, when two angles form a linear pair, their measures add up to \(180^{\circ}\).

Step2: Check each option

• Option 1: \(m\angle SQV + m\angle SQT = 180^{\circ}\) is incorrect as these angles do not form a linear pair.
• Option 2: \(m\angle SQV + m\angle VQT=m\angle VQT + m\angle ZRS\) is incorrect as there is no such relationship.
• Option 3: \(m\angle VQT + m\angle ZRS = 180^{\circ}\) is incorrect as these angles do not form a linear pair.
• Option 4: \(m\angle SQV + m\angle VQT = 180^{\circ}\) is correct as \(\angle SQV\) and \(\angle VQT\) form a linear pair.

Answer:

\(m\angle SQV + m\angle VQT = 180^{\circ}\)