Question 938170
<pre>
{{{drawing(400,400,-1.3,1.3,-1.3,1.3,

circle(0,0,1.01), 

line(cos(225*pi/180),sin(225*pi/180),cos(119*pi/180),sin(119*pi/180)),
line(cos(119*pi/180),sin(119*pi/180),cos(97*pi/180),sin(97*pi/180)),
line(cos(97*pi/180),sin(97*pi/180),cos(315*pi/180),sin(315*pi/180)),
line(cos(225*pi/180),sin(225*pi/180),cos(315*pi/180),sin(315*pi/180)),
locate(-.79,-.7,B),locate(-.55,.95,C),locate(-.15,1.08,D),
locate(.71,-.7,A), locate(-.64,-.55,6x+4),locate(-.48,.88,9x-1),
locate(.5,-.6,"64°")

 )}}}

A quadrilateral ABCD is cyclic if and only if its opposite 
angles are supplementary.

A and C are opposite angles, so they are supplementary

m&#8736;A + m&#8736;C = 180°
9x-1 + 64 = 180
    9x+63 = 180
       9x = 117
        x = 13°

m&#8736;B = 6x+4 = 6(13)+4 = 82°

B and D are opposite angles, so they are supplementary

m&#8736;B + m&#8736;D = 180°
82° + m&#8736;D = 180°
      m&#8736;D = 98°
      
Edwin</pre>