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Problem 12

# If $$\angle \mathrm{x}$$ has a measure of $$40^{\circ}$$ and $$\angle \mathrm{y}$$ has a measure of $$40^{\circ}$$, prove $\mathrm{m} \angle \mathrm{x}=\mathrm{m} \angle \mathrm{y}$ using the standard two column proof method.

Expert verified
Using the given information and the standard two-column proof method, we can prove that the measure of angle x is equal to the measure of angle y as follows: |#| Statement | Reason | |:-|:-----------|:----------| |1| m∠x = 40° | Given | |2| m∠y = 40° | Given | |3| m∠x = m∠y | Transitive Property of Equality| Since both angles have a measure of 40°, by the transitive property of equality, m∠x must be equal to m∠y.
See the step by step solution

## Step 1: State the given information

We are given that the measure of angle x is 40 degrees and the measure of angle y is 40 degrees. This can be written as: m∠x = 40° m∠y = 40° Step 2:

## Step 2: Write the proof in two-column format

Now we will prove that m∠x = m∠y using the two-column proof. |#| Statement | Reason | |:-|:-----------|:----------| |1| m∠x = 40° | Given | |2| m∠y = 40° | Given | |3| m∠x = m∠y | Transitive Property of Equality| Step 3:

## Step 3: Verify the proof

In the above two-column proof, we first used the given information (m∠x = 40° and m∠y = 40°) in steps 1 and 2. Then, we used the transitive property of equality to show that if m∠x = 40° and m∠y = 40°, then m∠x must be equal to m∠y in step 3. This proves that the measure of angle x is equal to the measure of angle y.

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