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.
On this exercise is asked you to find the measure in degrees of angle B. First of all, you have to find the value of x. To do this you have to select two angles, on this case angles B and D.
m<B+m<D=180 Substitute the given values for angles B and D
x+6x+19=180 Combine like terms
7x+19=180 Subtract 19 in both sides
7x=161 Divide by 7 in both sides to isolate x
x=23
Now that the value of x is known, you can substitute it into the expression representing angle B.
m<B=6x+19 Substitute the value of x previous found
m<B=6(23)+19 Multiply
m<B=138+19 Add
m<B=157
The measure of angle B is 157 degrees.
