What is the inverse of the following statement?
 

*If two angles are complementary, then the sum of the measures is 90.*


 

A.If two angles are complementary, then the sum of the measures is 90.

B.If the sum of the measures of two angles is 90, then the angles are supplementary.

C.If the sum of the measures of two angles is not 90, then the angles are not complementary.

D.If two angles are not complementary, then the sum of the measures is not 90.


The inverse of a conditional statement is formed by negating both the hypothesis and the conclusion of the original statement.

Given the original statement: "If two angles are complementary, then the sum of the measures is 90."

The inverse would be: "If two angles are **not** complementary, then the sum of the measures is **not** 90."

Therefore, the correct answer is **D.** If two angles are not complementary, then the sum of the measures is not 90.

Would you like more details or have any other questions?

Here are 5 related questions:

1. What is the converse of the statement?
2. How do you form the contrapositive of a statement?
3. Can you give an example of a statement and its inverse in geometry?
4. What is the difference between a statement and its negation?
5. How are inverse and contrapositive statements related?

**Tip:** Understanding the relationships between the original statement, its converse, inverse, and contrapositive helps in developing logical reasoning skills in geometry.

Learn about inverse statements in geometry with an example involving complementary angles. Explore how to form the inverse of a conditional statement and enhance your logical reasoning skills. Suitable for high school students.

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