Question

problem 8: (first taught in lesson 26) write the converse of this statement and decide whether it is true or false. then, select the correct answer. if two angles are supplementary, then the sum of their measures is 180. a if the measure of two angles is supplementary, then the measure of each angle is 180; false b c d e

Explanation:

To solve this, we first recall that the converse of a conditional statement "If \( p \), then \( q \)" is "If \( q \), then \( p \)".

Step 1: Identify \( p \) and \( q \) in the original statement

The original statement is: "If two angles are supplementary (\( p \)), then the sum of their measures is 180 (\( q \))".

Step 2: Write the converse

The converse swaps \( p \) and \( q \), so it becomes: "If the sum of the measures of two angles is 180, then the two angles are supplementary."

Step 3: Determine if the converse is true or false

By definition, supplementary angles are two angles whose measures add up to 180 degrees. So if the sum of two angles’ measures is 180, they must be supplementary. Thus, the converse is true.

(Note: The option shown in the image (Option A) is incorrect because it misinterprets the converse. The correct converse should relate the sum of measures to the angles being supplementary, not claim each angle is 180.)

But since the problem asks to write the converse and decide its truth value, the correct converse is "If the sum of the measures of two angles is 180, then the two angles are supplementary" and it is true.

However, if we assume the options were intended to have the correct converse (maybe a typo in the provided option), but based on the logical process:

The converse is "If the sum of the measures of two angles is 180, then the two angles are supplementary" and it is true.

If we strictly analyze the given option A: It misstates the converse (it says "the measure of each angle is 180" which is wrong), so the correct answer (if options were properly formatted) would have the converse as above and mark it true.

But since the problem’s option A is incorrect, perhaps there was a formatting error. Assuming the intended correct converse, the answer is that the converse is "If the sum of the measures of two angles is 180, then the two angles are supplementary" and it is true.

Answer:

To solve this, we first recall that the converse of a conditional statement "If \( p \), then \( q \)" is "If \( q \), then \( p \)".

Step 1: Identify \( p \) and \( q \) in the original statement

The original statement is: "If two angles are supplementary (\( p \)), then the sum of their measures is 180 (\( q \))".

Step 2: Write the converse

The converse swaps \( p \) and \( q \), so it becomes: "If the sum of the measures of two angles is 180, then the two angles are supplementary."

Step 3: Determine if the converse is true or false

By definition, supplementary angles are two angles whose measures add up to 180 degrees. So if the sum of two angles’ measures is 180, they must be supplementary. Thus, the converse is true.

(Note: The option shown in the image (Option A) is incorrect because it misinterprets the converse. The correct converse should relate the sum of measures to the angles being supplementary, not claim each angle is 180.)

But since the problem asks to write the converse and decide its truth value, the correct converse is "If the sum of the measures of two angles is 180, then the two angles are supplementary" and it is true.

However, if we assume the options were intended to have the correct converse (maybe a typo in the provided option), but based on the logical process:

The converse is "If the sum of the measures of two angles is 180, then the two angles are supplementary" and it is true.

If we strictly analyze the given option A: It misstates the converse (it says "the measure of each angle is 180" which is wrong), so the correct answer (if options were properly formatted) would have the converse as above and mark it true.

But since the problem’s option A is incorrect, perhaps there was a formatting error. Assuming the intended correct converse, the answer is that the converse is "If the sum of the measures of two angles is 180, then the two angles are supplementary" and it is true.