Lines BC and ED are parallel. They are intersected by transversal AE, in which point B lies between points and E. They are also intersected by transversal EC. Angle ABC measures 70 degrees. Angle CED measures 30 degrees.
Given: line BC is parallel to line ED
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∠BEC + m∠CED = m∠BED Angle Addition Postulate
m∠BEC + 30° = 70° Substitution Property of Equality
m∠BEC = 40° Subtraction Property of Equality
Which of the following accurately completes the missing statement and justification of the two-column proof?
m∠ABC = m∠CED; Corresponding Angles Theorem
m∠ABC = m∠CED; Alternate Interior Angles Theorem
m∠ABC = m∠BED; Corresponding Angles Theorem
m∠ABC = m∠BED; Alternate Interior Angles Theorem