Chapter 2, Problem 1RE

To determine

Whether the statement “In Fig 2.6, $\angle AOC$ is the complement of $\angle COB$” is true or false.

Answer to Problem 1RE

The statement “In Fig 2.6, $\angle AOC$ is the complement of $\angle COB$” is false.

Explanation of Solution

From the given figure it is observed that, the angle $\angle AOC$ and $\angle COB$ makes a straight line.

That is, the angles $\angle AOC$ and $\angle COB$ are supplementary angles.

Note that, if the sum of the measure of two angle is $180°$, then the angles are called supplementary angles. Each one is the supplement of the other.

This implies, $\angle AOC+\angle COB=180°$ which is not a complementary angles because the sum of the measure of two angle is $180°$.

Thus, the statement “In Fig 2.6, $\angle AOC$ is the complement of $\angle COB$” is false.