Given: line BC is parallel to line ED

Question

m∠ABC = 70°
m∠CED = 30°

Prove: m∠BEC = 40°

Statement Justification
line BC is parallel to line ED Given
m∠ABC = 70° Given
m∠CED = 30° Given
m∠ABC = m∠BED Corresponding Angles Theorem
m∠BEC + m∠CED = m∠BED Angle Addition Postulate

m∠BEC = 40° Subtraction Property of Equality

Which of the following accurately completes the missing statement and justification of the two-column proof?
m∠BEC + 30° = 70°; Substitution Property of Equality
m∠BEC + 30° = 70°; Addition Property of Equality
m∠BEC + 40° = 70°; Substitution Property of Equality
m∠BEC + 40° = 70°; Addition Property of Equality

Answer 1

To complete the missing statement and justification in the two-column proof, we can focus on the relationship established by previous steps.

1. From the given information and previous deductions, we had:

   • m∠ABC = m∠BED (from the Corresponding Angles Theorem since BC is parallel to ED)
   • So, m∠BED = 70°.

2. From m∠BEC + m∠CED = m∠BED (by the Angle Addition Postulate) and knowing m∠CED is 30°:

   • We can substitute to get m∠BEC + 30° = 70°.

3. This gives us the equation we need to prove m∠BEC:

   • m∠BEC + 30° = 70°.

4. Thus, we can subtract 30° from both sides to find m∠BEC:

   • m∠BEC = 70° - 30° = 40°.

So, the correct choice to complete the proof is:

m∠BEC + 30° = 70°; Substitution Property of Equality.