Q. 28 WE - Geometry

Question

Draw a line, $\overleftrightarrow{\mathit{A}\mathit{B}}$. Choose a point $\mathit{O}$ between $\mathit{A}$ and $\mathit{B}$. Use a protractor to investigate the following questions.

A careless person wrote, using the figure shown,  

$\mathit{m}\mathbf{\angle }\mathit{A}\mathit{O}\mathit{B}\mathbf{+}\mathit{m}\mathbf{\angle }\mathit{B}\mathit{O}\mathit{C}\mathbf{=}\mathit{m}\mathbf{\angle }\mathit{A}\mathit{O}\mathit{C}$.

What part of the Angle addition Postulate did that person overlook?

Step-by-Step Solution

Answer

The part of the angle addition Postulate the person overlooked is:

$\mathit{m}\mathbf{\angle }\mathit{A}\mathit{O}\mathit{B}\mathbf{+}\mathit{m}\mathbf{\angle }\mathit{B}\mathit{O}\mathit{C}\mathbf{+}\mathit{m}\mathbf{\angle }\mathit{A}\mathit{O}\mathit{C}\mathbf{=}{\mathbf{360}}^{\mathbf{\circ }}$

Step 1 - State the Angle addition postulate

The postulate state that if two angles are placed side by side, then the value of the resulting angle is equal to the sum of the original angles.

Step 2-Observe the diagram

As it can be seen from the figure that, $m\angle AOB+m\angle BOC\ne m\angle AOC$.

Because $\angle AOC$ is greater less than $180°$, also the sum of $\angle AOB$ and $\angle BOC$ is greater than $180°$.

Step 3 -State the conclusion

Therefore, the equation $m\angle AOB+m\angle BOC=m\angle AOC$ is not possible.

Since, the complete circle is $360°$, the correct equation thus formed will be $m\angle AOB+m\angle BOC+m\angle AOC=360°$ 

Therefore, the equation is $m\angle AOB+m\angle BOC+m\angle AOC=360°$.