Question

write the two conditional statements that form the following biconditional statement. two angles are supplementary if and only if the sum of their measures is 180 degrees. what are the two conditional statements that form the given biconditional statement? select all that apply. a. if the sum of their measures is not 180 degrees, then two angles are supplementary. b. if two angles are supplementary, then the sum of their measures is not 180 degrees. c. if the sum of their measures is 180 degrees, then two angles are supplementary. d. if two angles are supplementary, then the sum of their measures is 180 degrees.

Explanation:

A biconditional statement "p if and only if q" is equivalent to the two conditional statements "if p, then q" and "if q, then p". Here, p is "two angles are supplementary" and q is "the sum of their measures is 180 degrees".

• For option C: It is "if q, then p" (if the sum is 180, then angles are supplementary), which matches.
• For option D: It is "if p, then q" (if angles are supplementary, then sum is 180), which matches.
• Option A has a negative condition and incorrect conclusion.
• Option B has an incorrect conclusion (sum is not 180) for the given p.

Answer:

C. If the sum of their measures is 180 degrees, then two angles are supplementary.
D. If two angles are supplementary, then the sum of their measures is 180 degrees.