+9466 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.
\(\begin{array}{ccccccc} m\stackrel{\large\frown}{GK}& =& (9x-22)^{\circ}& =&(9(21)-22)^\circ&=&167^\circ\\~\\ m\stackrel{\large\frown}{HJ}& =& (5x-7)^{\circ}& =&(5(21)-7)^\circ&=&98^\circ\\~\\ m\stackrel{\large\frown}{HGJ}& =& m\stackrel{\large\frown}{HG}+m\stackrel{\large\frown}{GK}+m\stackrel{\large\frown}{KJ} & =& 61^\circ+167^\circ+34^\circ&=&262^\circ\\~\\ m\stackrel{\large\frown}{GKJ}&=&m\stackrel{\large\frown}{GK}+m\stackrel{\large\frown}{KJ} &=&167^\circ+34^\circ&=&201^\circ \end{array}\)
