Question

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

Answer 1

The missing statement and justification of the proof are:

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

Recall:

Angle Addition Postulate states that the sum of the two small angles that make up a larger angle will give the measure of the larger angle.

• From the image given:

$\angle BEC and \angle CED$ are smaller angles that makes up $\angle BED$.

• Therefore:

$m\angle BEC + m\angle CED = m\angle BED (Angle Addition Postulate)$

• Thus, the missing statement and justification in the proof would be:

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

Learn more about Angle Addition Postulate here:

https://brainly.com/question/18888627

Answer 2

Answer:

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

Step-by-step explanation:

Took the test :)