Question

what is the inverse of the following statement? \if an angle is acute, then it is less than 90 degrees.\ if an angle is not acute, then it is not less than 90 degrees. if an angle is less than 90 degrees, then it is acute. if an angle is not less than 90 degrees, then it is not acute. if an angle is acute, then it is not less than 90 degrees.

Explanation:

Step1: Recall the definition of inverse statement

For a conditional statement “If \(p\), then \(q\)” (\(p
ightarrow q\)), the inverse is “If \(
eg p\), then \(
eg q\)”

Let \(p\) be “an angle is acute” and \(q\) be “it is less than \(90\) degrees”

Step2: Find the inverse

The original statement is \(p
ightarrow q\). The inverse is \(
eg p
ightarrow
eg q\), which means “If an angle is not acute, then it is not less than \(90\) degrees”

Answer:

If an angle is not acute, then it is not less than 90 degrees.