Answer: Option C.
Step-by-step explanation:
Let as consider the below figure is attached below.
We know that angle between tangent and secant is half of difference of major and minor arcs.
[tex]\angle ABC=\dfrac{arc(AD)-arc(AC)}{2}[/tex]
[tex]3x+19=\dfrac{17x-3-91}{2}[/tex]
Multiply both sides by 2.
[tex]6x+38=17x-94[/tex]
[tex]38+94=17x-6x[/tex]
[tex]132=11x[/tex]
Divide both sides by 11.
[tex]12=x[/tex]
The value of x is 12.
[tex]arc(AD)=17(12)-3[/tex]
[tex]arc(AD)=204-3[/tex]
[tex]arc(AD)=201^{\circ}[/tex]
Now,
[tex]arc(DCA)=360^\circ-arc(AD)[/tex]
[tex]arc(DCA)=360^\circ-201^{\circ}[/tex]
[tex]m\widehat {DCA}=159^{\circ}[/tex]
Therefore, the correct option is C .
