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=77The measure of angle A is 77 degrees.
