Question

​ Quadrilateral ABCD ​ is inscribed in this circle.

What is the measure of angle C?

Please explain how you got the answer.

Answer 1

Consider this option:
1. using the property of the inscribed quadrilateral it is possible to make up the system of linear equations:
2.

`\left \{ {{A+C=180} \atop {B+D=180}} \right. \ =\ \textgreater \ \ \left \{ {{2x+3+C=180} \atop {3x+9+2x-4=180}} \right. \ =\ \textgreater \ \ \left \{ {{C=107} \atop {x=35}} \right.`

answer: 107°

Answer 2

The answer is as follows: