Quadrilateral abcd is inscribed in this circle. what is the measure of angle c? enter your answer in the box

1. The sum of the opposite angles of the quadrilateral ABCD that is inscribed in the circle, is 180°. Therefore, the sum of all the angles is 360°.

 2. As you can see, m∠B=(2x-1)° and m∠D=(3x-59)° are opposite angles, then:

 m∠B+m∠D=180°

 3. When you substitute the values of m∠B and m∠D into m∠B+m∠D=180°, you obtain:

 m∠B+m∠D=180°
 (2x-1)+(3x-59)=180°

 4. You must clear the "x", as below:

 (2x-1)+(3x-59)=180°
 5x-60=180
 x=48°

 5. Now, you can find the value of m∠A, m∠B and m∠D:

 m∠A=2x+4
 m∠A=2(48)+4
 m∠A=100°

 m∠B=2x-1
 m∠B=2(48)-1
 m∠B=95°

 m∠D=3x-59
 m∠D=3(48)-59
 m∠D=85°

 6. Therefore, the value of m∠C is:

 m∠A+m∠B+m∠C+m∠D=360°
 m∠C=360-m∠A-m∠B-m∠D
 m∠C=360°-100°-95°-85°
 m∠C=80°

 What is the measure of angle C?

 The answer is: 80°