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[tex]XCV \: \: angle = \frac{XWV \: \: arc}{2} \\ [/tex]
Multiply sides by 2
[tex]2 \: XCV \: \: angle = XWV \: \: arc[/tex]
[tex]XWV \: \: arc = 2 × XCV \: \: angle \\ [/tex]
[tex]XWV \: \: arc = 156°[/tex]
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[tex]XWV \: \: arc + VCX \: \: arc = 360° \\ [/tex]
[tex]156° + VCX \: \: arc = 360°[/tex]
Subtract sides 156°
[tex]-156° + 156° + VCX \: \: arc = -156° + 360° \\ [/tex]
[tex]VCX \: \: arc = 204°[/tex]
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[tex]XWV \: \: angle = \frac{XCV \: \: arc}{2} \\ [/tex]
[tex]17x = \frac{204}{2} \\ [/tex]
[tex]17x = 102[/tex]
Divide sides by 17
[tex] \frac{17x}{17} = \frac{102}{17} \\ [/tex]
[tex]x = 6[/tex]
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Sum of the interior angles of XWVC equal 360° .
Thus in XWVC :
[tex]X + W + V + C = 360°[/tex]
[tex](9y) + (17x) + (6y) + (78°) = 360° \\ [/tex]
[tex]15y + 17x + 78° = 360°[/tex]
[tex]15y + 17(6) + 78° = 360°[/tex]
[tex]15y + 102° + 78° = 360°[/tex]
[tex]15y + 180° = 360°[/tex]
Subtract sides 180°
[tex]15y + 180° - 180° = 360° - 180° \\ [/tex]
[tex]15y = 180°[/tex]
Divide sides by 15
[tex] \frac{15y}{15} = \frac{180}{15} \\ [/tex]
[tex]y = 12[/tex]
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[tex]X = 9y[/tex]
[tex]X = 9(12)[/tex]
[tex]X = 108°[/tex]
[tex]V = 6y[/tex]
[tex]V = 6(12)[/tex]
[tex]V = 72°[/tex]
[tex]W = 17x[/tex]
[tex]W = 17(6)[/tex]
[tex]W = 102°[/tex]
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