To solve this question we will have to make use of one of the properties of the inscribed quadrilateral. That property is: "Opposite angles in any quadrilateral inscribed in a circle are supplements of each other".
Thus, as we can see from the diagram given, [tex] \angle B+\angle D=180^{\circ} [/tex]
[tex] (2x+3)+(4x+3)=180^{\circ} [/tex]
[tex] \therefore 6x+6=180^{\circ} [/tex]
[tex] 6x=174^{\circ} [/tex]
[tex] \therefore x=\frac{174^{\circ}}{6} =28^{\circ} [/tex]
Thus, now that we know the value of x, we can easily find the value of the [tex] \angle C [/tex] because we know that:
[tex] \angle C=2x+1 [/tex]
[tex] \therefore \angle C=2(29^{\circ})+1=59^{\circ} [/tex]
Thus, [tex] \boldsymbol{59^{\circ}} [/tex] is the correct answer.
