Rewrite the definition "Linear angles are supplementary" in biconditional form The angles are linear angles if and only if they are supplementary. If the angles are linear angles only if they are supplementary. If the angles are linear angles, then they are supplementary. If and only if the angles are linear angles, if and only if they are supplementary.

Question

Mathematics

Makena Bray

8 July, 08:26

Rewrite the definition "Linear angles are supplementary" in biconditional form The angles are linear angles if and only if they are supplementary. If the angles are linear angles only if they are supplementary. If the angles are linear angles, then they are supplementary. If and only if the angles are linear angles, if and only if they are supplementary.

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Answers (1)

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Javion Everett · Answer 1

3. If angles are linear, then they are supplementary.

Step-by-step explanation:

We are given that a definition

''Linear angles are supplementary"'.

We have to rewrite definition in bi-conditional form

1. The angles are linear angles if and only if they are supplementary.

If given that angles are linear

Then, the angles should be supplementary.

But, if given that angles are supplementary

Then, it is not necessary that angles are linear because sum of interior angles are also supplementary.

Hence, option is false.

2. If angles are linear angles only if they are supplementary.

It is also false. Because supplementary angles need not be linear angles They can be interior angles.

Hence, option is false.

3. If angles are linear, then they are supplementary.

If the angles are linear angles then the sum is always 180 degrees and the angles should be supplementary angles. Hence, option is correct.

4. If and only the angles are linear angles, if and only if they are supplementary. It is not correct form of statement, hence, option is false.