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°
