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∠abc = m∠bed corresponding angles theorem
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∠bec + m∠ced = m∠bed; definition of a linear pair
m∠abc + m∠bec = m∠bed; angle addition postulate
m∠abc + m∠bec = m∠bed; definition of a linear pair
m∠bec + m∠ced = m∠bed; angle addition postulate

m∠BEC + m∠CED = m∠BED; Angle Addition Postulate

Step-by-step explanation:

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∠ABC = m∠BED Corresponding Angles Theorem

m∠BEC + m∠CED = m∠BED Angle Addition Postulate

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

m∠BEC = 40° Subtraction Property of Equality

m∠BEC + m∠CED = m∠BED; Angle Addition Postulate

Step-by-step explanation:

For example : If ∠MON and ∠NOK are joined such that NO is the common line segment between then then the new angle will be ∠MOK or ∠KOM.

In given figure , m∠BEC and m∠CED are joined and they have common line segment CE , then the new angle m∠BED= m∠BEC + m∠CED

Hence, the correct statement that completes the given proof :

m∠BEC + m∠CED = m∠BED; Angle Addition Postulate

(-5,-28)

i graphed to on desmos.