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

Question

23-08-2021
Mathematics

contestada

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

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olayemiolakunle65 olayemiolakunle65 · Answer 1 · 2021-09-04T21:15:55+02:00

Considering the angle theorems, the appropriate answer to the question is option D. m∠BEC + m∠CED = m∠BED; Angle Addition Postulate

In the diagram, lines BC and ED are parallel and both were intersected by a transversal AE. Thus it can be observed that:

m<ABC = BED = [tex]70^{o}[/tex] (corresponding angle theorem)

But,

m<BEC + m<CED = m<BED (angle addition postulate)

with m<CED = [tex]30^{o}[/tex], and m<BED = [tex]70^{o}[/tex]

So that,

m<BEC + [tex]30^{o}[/tex] = [tex]70^{o}[/tex]

m<BEC = [tex]70^{o}[/tex] - [tex]30^{o}[/tex]

= [tex]40^{o}[/tex]

m<BEC = [tex]40^{o}[/tex]

Since linear pair are two angles that add up to [tex]180^{o}[/tex]. Therefore the required answer is option D.

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

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