Chapter 2.3, Problem 4ST1

To determine

To state: A counterexample to disprove the given statement

Answer to Problem 4ST1

"If $m\angle A$ is less than ${100}^{\circ }$ , then $\angle A$ is an acute angle"

The counterexample is given below:

  $m\angle A={91}^{\circ }$

Explanation of Solution

Given information:

"If $m\angle A$ is less than ${100}^{\circ }$ , then $\angle A$ is an acute angle"

Consider the statement:

"If $m\angle A$ is less than ${100}^{\circ }$ , then $\angle A$ is an acute angle"

An example to disprove the above statement is as follows:

Consider $m\angle A={91}^{\circ }$

So, $m\angle A<{100}^{\circ }$

And also

  $\angle A>{90}^{\circ }$ Therefore, $\angle A$ is not an acute angle

Thus, "If $m\angle A$ is less than ${100}^{\circ }$ , then $\angle A$ is an acute angle"