Answer:
[tex]a) x=15\\b) AD\ is\ not\ parallel\ tp BC[/tex]
Step-by-step explanation:
[tex]As\ we\ know\ that,\\Angle\ D=3x\\Angle\ A=2x\\Angle\ B=90\\Angle\ C=x\\The\ Angle\ Sum\ Property\ Of\ A\ Quadrilateral\ states\ that\ the\ sum\ of\ all\\ the\ interior\ angles\ of\ a\ quadrilateral\ is\ 180.\\Hence,\\ \angle D+ \angle A + \angle B + \angle C=360\\3x+2x+90+x=180\\3x+2x+x=180-90\\6x=90\\x=15\\Hence, x=15[/tex]
[tex]Hence,\\As\ Angle\ A\ and\ Angle\ B\ are\ co-interior\ angles, if\ they\ are\\ supplementary\ then\ AD \parallel BC.\ Lets\ check\ that\ out.\\Hence,\\Angle\ A=2x=2*15=30\\Angle\ B=90\ [Given]\\Hence,\\As\ 90+30\neq 180,\\Angle\ A +Angle\ B\neq 180\\Hence,\\As\ Angle\ A and\ Angle\ B\ are\ not\ supplementary, AD\ will\ not\ be\ parallel\ to\ CB.[/tex]
