question
what is the inverse of the following statement.
if ( mangle1 + mangle2 = 180 ), then the angles are supplementary.
answer
if two angles are supplementary, then ( mangle1 + mangle2 = 180 )
if ( mangle1 + mangle2 = 180 ), then the angles are not supplementary.
none of the above.
if two angles are not supplementary, then ( mangle1 + mangle2
eq 180 )
if ( mangle1 + mangle2
eq 180 ), then the angles are not supplementary.

Question

Accepted Answer

# Explanation:
To find the inverse of a conditional statement "If $ p $, then $ q $", we negate both the hypothesis ($ p $) and the conclusion ($ q $). The original statement is: "If $ m\angle1 + m\angle2 = 180 $, then the angles are supplementary." Here, $ p $ is $ m\angle1 + m\angle2 = 180 $ and $ q $ is "the angles are supplementary."

## Step 1: Identify $ p $ and $ q $
- Hypothesis ($ p $): $ m\angle1 + m\angle2 = 180 $
- Conclusion ($ q $): The angles are supplementary

## Step 2: Negate $ p $ and $ q $
- Negation of $ p $ ($
eg p $): $ m\angle1 + m\angle2
eq 180 $
- Negation of $ q $ ($
eg q $): The angles are not supplementary

## Step 3: Form the inverse
The inverse of "If $ p $, then $ q $" is "If $
eg p $, then $
eg q $". So substituting the negations, we get: "If $ m\angle1 + m\angle2
eq 180 $, then the angles are not supplementary." Wait, looking at the options, let's re - evaluate. Wait, maybe I made a mistake in the options. Wait, the options given:

Wait, the original statement: $ p $: $ m\angle1 + m\angle2 = 180 $, $ q $: angles are supplementary.

Inverse is $
eg p
ightarrow
eg q $, which is "If $ m\angle1 + m\angle2
eq180 $, then the angles are not supplementary". But looking at the options, one of the options is "If two angles are not supplementary, then $ m\angle1 + m\angle2
eq180 $"? Wait, no, let's check the options again.

Wait, the options:

1. If two angles are supplementary, then $ m\angle1 + m\angle2 = 180 $ (this is the converse)
2. If $ m\angle1 + m\angle2 = 180 $, then the angles are not supplementary (this is a contradiction, not inverse)
3. If two angles are not supplementary, then $ m\angle1 + m\angle2
eq180 $ (this is the contrapositive)
4. If $ m\angle1 + m\angle2 = 180 $, then the angles are not supplementary (same as option 2)
5. None of the above.

Wait, my initial calculation of the inverse was wrong. Wait, the inverse of "If $ p $, then $ q $" is "If not $ p $, then not $ q $". So $ p $ is $ m\angle1 + m\angle2 = 180 $, so not $ p $ is $ m\angle1 + m\angle2
eq180 $, and not $ q $ is angles are not supplementary. So the inverse should be "If $ m\angle1 + m\angle2
eq180 $, then the angles are not supplementary". But none of the options have this? Wait, maybe there is a typo in the options. Wait, looking at the options again, one of the options is "If two angles are not supplementary, then $ m\angle1 + m\angle2
eq180 $" - that is the contrapositive. The converse is "If $ q $, then $ p $". The inverse is "If not $ p $, then not $ q $". Since none of the options match the correct inverse, the answer is "None of the above".

# Answer:
None of the above.

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QUESTION IMAGE

Question

Explanation:

Step 1: Identify \( p \) and \( q \)

Step 2: Negate \( p \) and \( q \)

Step 3: Form the inverse

Answer: