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[tex](9x + 17) +2 \times ( 5x + 15 ) + (6x - 12) = 360 \\ [/tex]
[tex]9x + 17 + 10x + 30 + 6x - 12 = 360 \\ [/tex]
[tex]9x + 10x + 6x + 17 + 30 - 12 = 360 \\ [/tex]
Collect like terms
[tex]25x + 35 = 360[/tex]
Subtract sides 35
[tex]25x + 35 - 35 = 360 - 35[/tex]
[tex]25x = 325[/tex]
Divide sides by 25
[tex] \frac{25x}{25} = \frac{325}{25} \\ [/tex]
[tex]x = 13[/tex]
Thus ;
[tex]RQ \: \: arc =2 \times (5x + 15)[/tex]
[tex]RQ \: \: arc = 10x + 30[/tex]
[tex]RQ \: \: arc = 10(13) + 30[/tex]
[tex]RQ \: \: arc = 130 + 30[/tex]
[tex]RQ \: \: arc = 160°[/tex]
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