Question

Quadrilateral ABCD is inscribed in circle O.

Answer 1

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, $\angle B+\angle D=180^{\circ}$

$(2x+3)+(4x+3)=180^{\circ}$

$\therefore 6x+6=180^{\circ}$

$6x=174^{\circ}$

$\therefore x=\frac{174^{\circ}}{6} =28^{\circ}$

Thus, now that we know the value of x, we can easily find the value of the $\angle C$ because we know that:

$\angle C=2x+1$

$\therefore \angle C=2(29^{\circ})+1=59^{\circ}$

Thus, $\boldsymbol{59^{\circ}}$ is the correct answer.

Answer 2

Angle C would equal 59 degrees