Chapter 1.4, Problem 28WE

To determine

To find: The part of the angle addition postulate the person overlook.

Answer to Problem 28WE

  $m\angle \text{AOB+}m\angle \text{BOC}+m\angle \text{AOC}={360}^{\circ }$

Explanation of Solution

Given information:

A careless person wrote, using the figure shown,

  $\text{m}\angle \text{AOB+m}\angle \text{BOC}\text{=}\text{m}\angle \text{AOC}$

Formula used:

  $\angle \text{AOC}$ is greater less than 180°, also the sum of $\angle \text{AOB}$ and $\angle BOC$ is greater than 180°

Calculation:

Refer to the figure given in the text book:

Consider the Angle Addition Postulate:

As it can be seen from the figure it can be observe that

  $\text{m}\angle \text{AOB}\text{+}\text{m}\angle \text{BOC}\ne \text{m}\angle \text{AOC}$

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

Therefore the given equation is not possible.

Therefore, the complete circle is 360°.

Thus, the equation is;

  $m\angle \text{AOB+}m\angle \text{BOC}+m\angle \text{AOC}={360}^{\circ }$

Conclusion:

  $m\angle \text{AOB+}m\angle \text{BOC}+m\angle \text{AOC}={360}^{\circ }$