Chapter 2, Problem 12CR

To determine

To name: the definition, postulate, or theorem that justifies the given statement.

Answer to Problem 12CR

  $\angle DOE=32°,\angle BOA=32°$ and $\angle AOC=112°$ .

Explanation of Solution

Given information:

  $\angle BOC$ is a right angle and $m\angle COD=58°$ , then $m\angle DOE=--,m\angle BOA=--,$ and $m\angle AOC=--$ .

Given figure,

  

Calculation:

Consider the figure,

  

Consider the following statement,

  $\angle BOC=90°,\angle COD=58°$

Note that, $\angle BOC=\angle COE=90°$

Therefore,

  $\begin{array}{c}\angle COD+\angle DOE=90°\\ 58°+\angle DOE=90°\\ \angle DOE=32°\end{array}$

And $\angle DOE=\angle BOA$ since, both are vertically opposite angle.

And

  $\begin{array}{c}\angle AOC=\angle AOB+\angle BOC\\ =32°+90°\\ =112°\end{array}$

Therefore, $\angle DOE=32°,\angle BOA=32°$ and $\angle AOC=112°$ .