Question

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°.
help me solve...

Explanation:

To solve this, we first need to identify the hypothesis. In a conditional statement (though here the hypothesis is likely the statement "A polygon is a regular hexagon" from the context, as we're negating the hypothesis, not the conclusion). The negation of a statement \( P \) (here \( P \): "A polygon is a regular hexagon") is \(
eg P \), which means the opposite. So the negation of "A polygon is a regular hexagon" is "A polygon is not a regular hexagon".

Looking at the options:

• Option A is a conditional statement, not a negation of a hypothesis.
• Option B is a conditional with incorrect logic.
• Option C is the original hypothesis, not its negation.
• Option D: "A polygon is not a regular hexagon" is the negation of the hypothesis "A polygon is a regular hexagon".
• Option E is a conditional, not a negation of the hypothesis.
• Option F is negating the conclusion (about angles), not the hypothesis.
• Option G is the conclusion (about angles), not related to negating the hypothesis.

Answer:

D. A polygon is not a regular hexagon.