Question

Quadrilateral ABCD ​ is inscribed in a circle.

Answer 1

The meaning of a quadrilateral inscribed in a circle is that the angles on the opposite vertices are supplementary or in other words equals to 180 degrees.

In this exercise it is asked you to find the measure in degrees of angle A. First of all, you have to find the value of x. To do this you have to select two angles on this case angles A and C.

m<A+m<C=180          Substitute the values of angles A and C
2x+9+3x+1=180          Combine like terms       
        5x+10=180          Subtract in both sides by 10                           
              5x=170          Divide in both sides by 5 to isolate x               
                x= 34

Now that the value of x is known, you can substitute it into the expression representing angle A.

m<A=2x+9
m<A=2(34)+9
m<A=77

The measure of angle A is 77 degrees.