Question

What is the missing statement for step 5 in the two-column proof?

Step Statements Reasons
1 segment UV is parallel to segment WZ Given
2 Points S, Q, R, and T all lie on the same line. Given
3 m∠SQT = 180° Definition of a Straight Angle
4 m∠SQV + m∠VQT = m∠SQT Angle Addition Postulate
5 _________________
6 m∠VQT + m∠ZRS = 180° Same-Side Interior Angles Theorem
7 m∠SQV + m∠VQT = m∠VQT + m∠ZRS Substitution Property of Equality
8 m∠SQV + m∠VQT − m∠VQT = m∠VQT + m∠ZRS − m∠VQT
m∠SQV = m∠ZRS Subtraction Property of Equality
∠SQV ≅ ∠ZRS Definition of Congruency
A. m∠SQV + m∠VQT = 180°
B. m∠SQV = m∠SQT
C. m∠SQV + m∠SQT = m∠VQT
D. m∠SQV + m∠SQT = 180°

Answer 1

The missing statement for step 5 in the two-column proof is A. m∠SQV + m∠VQT = 180°, as it logically follows from the angle addition postulate and the definition of a straight angle.

Step-by-step explanation:

The correct missing statement for step 5 in the two-column proof is A. m∠SQV + m∠VQT = 180°. This is because the angle addition postulate (step 4) asserts that the sum of the measures of m∠SQV and m∠VQT equals the measure of m∠SQT, which has already been established to be a straight angle with a measure of 180° (step 3). Therefore, the measures of angles SQV and VQT must add up to 180°, forming a straight line.