Question

Write the inverse form of the conditional statement: "Supplementary angles sum to 180 degrees."

a) "If supplementary angles don't sum to 180 degrees, then they are not supplementary."

b) "If supplementary angles sum to 180 degrees, then they are supplementary."

c) "Supplementary angles sum to 180 degrees, but this may not always be the case."

d) "Supplementary angles don't necessarily sum to 180 degrees."

Answer 1

The inverse form of the conditional statement "Supplementary angles sum to 180 degrees." is: (option B) "If supplementary angles sum to 180 degrees, then they are supplementary."

Step-by-step explanation:

The inverse form of the conditional statement: "Supplementary angles sum to 180 degrees." is:

b) "If supplementary angles sum to 180 degrees, then they are supplementary."

To find the inverse of a conditional statement, you negate both the hypothesis (the "if" part) and the conclusion (the "then" part). In this case, the original statement was "Supplementary angles sum to 180 degrees." In the inverse statement, we negate the original statement: "Supplementary angles do not sum to 180 degrees."

Answer 2

The inverse of the given conditional statement is option a) 'If supplementary angles don't sum to 180 degrees, then they are not supplementary.' This is found by negating both the antecedent and consequent of the original conditional statement.

Step-by-step explanation:

The inverse form of the conditional statement "Supplementary angles sum to 180 degrees" is that if two angles do not sum to 180 degrees, then they are not supplementary angles. Therefore, the correct answer from the provided options is:
a) "If supplementary angles don't sum to 180 degrees, then they are not supplementary."

Conditionals have an antecedent followed by a consequent. Here, the antecedent is the non-summing to 180 degrees, and the consequent is that angles are not supplementary. To logically invert a conditional, one must negate both the antecedent and the consequent. Therefore, if it is not true that the angles sum to 180 degrees (negation of the antecedent), it cannot be true that they are supplementary (negation of the consequent).