Question

write the negation of the hypothesis and the negation of the conclusion for the conditional. if a polygon’s interior angle measures total 1,440°, then the polygon is a decagon. what is the negation of the conclusion? a. if a polygon is a decagon, then the polygon’s interior angle measures total 1,440° b. a polygon is a decagon. c. if a polygon’s interior angle measures total 1,440°, then the polygon is not a decagon. d. a polygon’s interior angle measures total 1,440° e. a polygon is not a decagon. f. a polygon’s interior angle measures do not total 1,440° g. if a polygon’s interior angle measures do not total 1,440°, then the polygon is a decagon

Explanation:

The conclusion of the conditional statement "If a polygon’s interior angle measures total \(1,440^\circ\), then the polygon is a decagon" is "the polygon is a decagon". The negation of a statement "P" is "not P". So the negation of "the polygon is a decagon" is "the polygon is not a decagon". Looking at the options, option E states "A polygon is not a decagon", which matches the negation of the conclusion.

Answer:

E. A polygon is not a decagon.