Chapter 2.1, Problem 42PPS

To determine

To evaluate the given statement

Explanation of Solution

Given information:

If $\angle 2$ and $\angle 3$ are supplementary angles, then $\angle 2$ and $\angle 3$ form a linear pair

Proof:

Let the figure be as given below,

Adding $\angle 2$ and $\angle 3$ ,

  $90+90$

On solving,

  $180$

Since, the sum of $\angle 2$ and $\angle 3$ 180, therefore they are supplementary angles.

But concluding from the figure, $\angle 2$ and $\angle 3$ are not linear angles.

Hence, the given statement “If $\angle 2$ and $\angle 3$ are supplementary angles, then $\angle 2$ and $\angle 3$ form a linear pair” is false.

Hence, proved