A biconditional statement is one that can be expressed in the form "P if and only if Q," meaning that both the conditional statement "If P, then Q" and its converse "If Q, then P" are true.
Let's analyze each of the statements to see if they can be written as biconditionals:
A. If you want to buy clothes, then you go to the mall.
This statement isn't necessarily true in reverse. Just because you go to the mall doesn't mean you are specifically wanting to buy clothes, as you could go for various other reasons. Therefore, this cannot be expressed as a biconditional.
B. If the sum of the measures of two angles is 180, then the angles are supplementary.
This statement can be reversed: if two angles are supplementary, then their measures sum to 180. Both statements are true, making this a valid biconditional.
C. If a number is divisible by 10, then it is divisible by 5.
This can be reversed: if a number is divisible by 5, it doesn't necessarily follow that it is divisible by 10, as numbers like 5 and 15 contradict this. Thus, this cannot be written as a biconditional.
D. If a polygon is a square, then it has four right angles.
This can also be reversed: if a polygon has four right angles, then it is a square. However, this is not true since a rectangle also has four right angles. Thus, this cannot be expressed as a biconditional.
The only conditional statement that can be expressed as a biconditional is:
B. If the sum of the measures of two angles is 180, then the angles are supplementary.