Question

Is the following definition of supplementary reversible? If yes, write it as a true biconditional. Supplementary angles are two angles whose measures sum to 180°. (1 point) Yes, if angles are supplementary, then their measures sum to 180°. Yes, angles are supplementary if (and only if) their measures sum to 180°. Yes, angles are supplementary if their measures sum to 180°. The statement is not reversible.

Answer 1

Yes, if angles are supplementary if and only if their measure sum to 180 degrees.

Explanation:

We are given definition of supplementary angles

Supplementary angles are two angles whose measures sum to 180 degrees.

We have to find that definition of supplementary angles is reversible or not.

If yes , then we have to write in true bi-conditional.

If sum of two angles is equal to 180 degrees then the angles are supplementary angles.

If the angles are supplementary then their sum is equal to 180 degrees.

Therefore, it is reversible.

Biconditional statement: if p, then q and if q, then p.

`p\Leftrightarrow`

Answer: Yes, if angles are supplementary if and only if their measure sum to 180 degrees.

Answer 2

Yes, angles are supplementary if (and only if) their measures sum to 180°

Explanation:

Well, let's look at the definition:

Supplementary angles are two angles whose measures sum to 180°

A biconditional statement is a conjunction of two implications. Like this:

1. If Two angles are supplementary then whose measures sum to 180º

(p→q)

2.If their measures sum to 180º then two angles are supplementary

(q→p)

3. Two angles are supplementary if and only if whose measures sum to 180º

(p↔q)

(p↔q)=(p→q)^(p→q)

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We can say that this Biconditional Statement (p↔q) the Hypothesis p and the Conclusion q is reversible because if we change the order of the operands to

q ↔p the Logical value remains the same as p↔q, i.e.

"If their measures sum to 180º then two angles are supplementary."