Respuesta :

Answer:  Choice A

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Explanation:

We start with [tex]m\angle\text{BEC}+m\angle\text{CED}=m\angle\text{BED}[/tex] which is the line just above the blank line.

Then we replace the angle CED with 30 and angle BED with 70. This is the substitution rule in action. Think of it like a substitute teacher taking a temporary place of the actual teacher.

So after using the substitution rule, we get [tex]m\angle\text{BEC}+30^{\circ}=70^{\circ}[/tex] showing why choice A is the answer.

varshamittal029

m∠BEC+m∠CED=m∠BED (Addition Property of Equality) is the missing statement in the problem.

What is Corresponding angles property?

This property says that Corresponding angles are equal.

How to prove?

In the given figure observe that

m∠ABC=m∠BED because they are corresponding angles.

i.e. m∠ABC=m∠BED=70°

Then since, m∠BED=m∠BEC+m∠CED

⇒70°=m∠BEC+30° from the diagram

⇒m∠BEC=70°-30°=40°

Proof:

BC is parallel to 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+m∠CED=m∠BED (Addition Property of Equality)

m∠BEC=40° (Subtraction Property of Equality)

So, m∠BEC+m∠CED=m∠BED (Addition Property of Equality) is the missing statement

Learn more about Corresponding Angles Theorem here-

brainly.com/question/16987080

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