Question

write the negation of the hypothesis and the negation of the conclusion for the conditional. if a polygon has angles that all measure 120°, then the polygon is a regular hexagon. what is the negation of the hypothesis? a. if a polygon is a regular hexagon, then the polygon has angles that all measure 120°. b. if a polygon does not have angles that all measure 120°, then the polygon is a regular hexagon. c. a polygon is a regular hexagon. d. a polygon is not a regular hexagon. e. if a polygon has angles that all measure 120°, then the polygon is not a regular hexagon. f. a polygon does not have angles that all measure 120°. g. a polygon has angles that all measure 120°.

Explanation:

The hypothesis of the conditional statement "If a polygon has angles that all measure \(120^\circ\), then the polygon is a regular hexagon" is "a polygon has angles that all measure \(120^\circ\)". The negation of a statement \(P\) is "not \(P\)". So the negation of the hypothesis is "a polygon does not have angles that all measure \(120^\circ\)". Looking at the options, option F matches this description.

Answer:

F. A polygon does not have angles that all measure \(120^\circ\)