3.  match the following reasons with the statements to complete the following proof. given: ad is a straight line and m cbd = m dbe to prove: m angle abc + m angle dbe = 180°. (pic here) 1. m angle cbd = m angle dbe 2. abc, cbd are supplementary 3. m angle abc + m angle cbd = 180° 4. m angle abc + m angle dbe = 180° a. given b. definition of supplementary c. substitution d. sides in opposite rays

Given: AD is a straight line and m CBD = m DBE

To Prove: m angle ABC + m angle DBE = 180°.

Proof:  First statement is :

1. m angle CBD = m angle DBE

We already given that. So the correct reason for this statement is A. Given.

Second statement :

2. ABC, CBD are supplementary.

Because exterior sides in opposite rays are making supplementary (sum upto 180). Therefore, reason for second statement is : D. ...exterior sides in opposite rays.

Third statement :

3. m angle ABC + m angle CBD = 180°

Angles ABC and CBD are add upto 180 degree by supplementary angles defination.

Therefore, reason for 3rd statement is : B. Definition of supplementary .

Fourth statement:

4. m angle ABC + m angle DBE = 180°

On substituting m angle CBD  = m angle DBE , we get  m angle ABC + m angle DBE = 180.

Therefore, 4th reason would be : C. Substitution .

Given: AD is a straight line and m CBD = m DBE

To Prove: m angle ABC + m angle DBE = 180°.

Proof:  First statement is :

1. m angle CBD = m angle DBE

We already given that. So the correct reason for this statement is A. Given.

Second statement :

2. ABC, CBD are supplementary.

Because exterior sides in opposite rays are making supplementary (sum upto 180). Therefore, reason for second statement is : D. ...exterior sides in opposite rays.

Third statement :

3. m angle ABC + m angle CBD = 180°

Angles ABC and CBD are add upto 180 degree by supplementary angles defination.

Therefore, reason for 3rd statement is : B. Definition of supplementary .

Fourth statement:

4. m angle ABC + m angle DBE = 180°

On substituting m angle CBD  = m angle DBE , we get  m angle ABC + m angle DBE = 180.

Therefore, 4th reason would be : C. Substitution .

Step-by-step explanation:

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