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Copy everything shown and complete the proof of theorem 2-7 for the case where two angles are supplements of the same angle.

Given:∠1 and∠5 are supplementary;∠3 and∠5 are supplementary.

Prove: 13

Short Answer

Expert verified

The complete proof table is:

Statements

Reasons

∠1 and∠5 are supplementary.

∠3 and∠5 are supplementary.

GIven

m1+m5=180;m3+m5=180


As,∠1 and∠5 are supplementary angles and

∠3 and ∠5 are supplementary angles

m1+m5=m3+m5

Substitution property

m5=m5

Reflexive property

m1=m3or13

Solve the equation m1+m5=m3+m5.

Step by step solution

01

Step 1. Observe the given diagram.

The given diagram is:

02

Step 2. Description of step.

It is being given that∠1 and∠5 are supplementary and∠3 and∠5 are supplementary.

As, and are supplementary angles, therefore the sum of the angles∠1 and∠5 is 180°.

Therefore, m1+m5=180.

As,∠3 and∠5 are supplementary angles, therefore the sum of the angles∠3 and∠5 is 180°.

Therefore, m3+m5=180.

Now, by using the substitution property it can be obtained that:

m1+m5=m3+m5

Therefore, it can be obtained that:

m1+m5=m3+m5m1=m313

Hence proved.

03

Step 3. Complete the proof table.

Statements

Reasons

∠1 and∠5 are supplementary.

∠3 and∠5 are supplementary.

GIven

m1+m5=180;m3+m5=180


As,∠1 and∠5 are supplementary angles and

∠3 and∠5 are supplementary angles

m1+m5=m3+m5

Substitution property

m5=m5

Reflexive property

m1=m3or13

Solve the equation m1+m5=m3+m5.

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