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Can somone help me solve this? I am lost. Thanks!

 

 Sep 25, 2020
 #1
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The sum of the measures of all the arcs in a circle is  360°

 

So... looking at the circle in problem #9....we can make the following equation:

 

61°   +   (5x - 7)°   +   34°   +   (9x - 22)°   =   360°

                                                                                Remove the degree sign from every term.

61   +   5x - 7   +   34   +   9x - 22   =   360

                                                                                Combine like terms.

14x   +  66   =  360

                                   Subtract  66  from both sides of the equation.

14x   =   294

                                   Divide both sides of the equation by  14

x   =   21

 

Now that we know what  x  is, we can find the measures of all the arcs.

 

\(\begin{array}{ccccccc} m\stackrel{\large\frown}{GK}& =& (9x-22)^{\circ}& =&(9(21)-22)^\circ&=&167^\circ\\~\\ m\stackrel{\large\frown}{HJ}& =& (5x-7)^{\circ}& =&(5(21)-7)^\circ&=&98^\circ\\~\\ m\stackrel{\large\frown}{HGJ}& =& m\stackrel{\large\frown}{HG}+m\stackrel{\large\frown}{GK}+m\stackrel{\large\frown}{KJ} & =& 61^\circ+167^\circ+34^\circ&=&262^\circ\\~\\ m\stackrel{\large\frown}{GKJ}&=&m\stackrel{\large\frown}{GK}+m\stackrel{\large\frown}{KJ} &=&167^\circ+34^\circ&=&201^\circ \end{array}\)

 Sep 25, 2020

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