Chapter 2.1, Problem 20WE

To determine

To state: The converse of statement and state whether it is true or false

Answer to Problem 20WE

The statement is true.

The converse of the given statement is false

Explanation of Solution

Given information:

The given statement is:

"If $m\angle T=40$ then $\angle T$ is not obtuse

"If $m\angle T=40$ then $\angle T$ is not obtuse

Here $\angle T$ is below ${90}^{\circ }$

That is, $\angle T$ is not obtuse.

Therefore, the statement is true.

Consider $p$ is $″m\angle T=40″$ and $q$ is $″\angle T$ is not obtuse”

The converse is of the form "if $q$ ,then $p^{″}$

Therefore, the converse of the given statement is;

If $\angle T$ is not obtuse then $m\angle T=40$

Here, $\angle T$ is not obtuse

Then, $m\angle T$ is between $0^{\circ }$ and ${90}^{\circ }$

That is, may be any value between $0^{\circ }$ and ${90}^{\circ }$

Therefore, the converse of the given statement is false.