select the statement that is the inverse of the following statement: if a polygon is equiangular, then all its interior angles have the same measure. answer if a polygon is equiangular, then all its interior angles don’t have the same measure. if a polygon isn’t equiangular, then all its interior angles don’t have the same measure. if all a polygon’s interior angles have the same measure, then it is equiangular. if all a polygon’s interior angles don’t have the same measure, then it isn’t equiangular.

Question

Accepted Answer

To determine the inverse of a conditional statement "If $ p $, then $ q $", we negate both the hypothesis ($ p $) and the conclusion ($ q $). The original statement is: "If a polygon is equiangular, then all its interior angles have the same measure." Here, $ p $ is "a polygon is equiangular" and $ q $ is "all its interior angles have the same measure."

### Step 1: Identify the hypothesis and conclusion
- Hypothesis ($ p $): A polygon is equiangular.
- Conclusion ($ q $): All its interior angles have the same measure.

### Step 2: Negate the hypothesis and the conclusion
- Negation of $ p $ ($
eg p $): A polygon isn't equiangular.
- Negation of $ q $ ($
eg q $): All its interior angles don't have the same measure.

### Step 3: Form the inverse statement
The inverse of "If $ p $, then $ q $" is "If $
eg p $, then $
eg q $". Substituting the negated hypothesis and conclusion, we get: "If a polygon isn't equiangular, then all its interior angles don't have the same measure."

# Brief Explanations:
The inverse of a conditional statement "If $ p $, then $ q $" is formed by negating both the hypothesis ($ p $) and the conclusion ($ q $). For the statement "If a polygon is equiangular, then all its interior angles have the same measure", the hypothesis ($ p $) is "a polygon is equiangular" (negated to "a polygon isn't equiangular") and the conclusion ($ q $) is "all its interior angles have the same measure" (negated to "all its interior angles don't have the same measure"). Combining these negations gives the inverse statement.
# Answer:
If a polygon isn't equiangular, then all its interior angles don't have the same measure.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step 1: Identify the hypothesis and conclusion

Step 2: Negate the hypothesis and the conclusion

Step 3: Form the inverse statement

Answer: