Question 860018
The opposite angle is 98° by the <b>Opposite Angles of Cyclic Quadrilaterals Conjecture</b>.
 
If you don't know what the Opposite Angles of Cyclic Quadrilaterals Conjecture is, it is that the opposite angles of cyclic quadrilaterals are supplementary. 
 
To prove this, take a circle. The two opposite angles in the quadrilateral are the inscribed angles of two arcs. Those arcs comprise the entire circle.
 
Therefore, as the measure of an inscribed angle is half that of the arc it defines, the two angles add up to 180°.
 
This conjecture has a weird proof; if you would like to have more clarification, feel free to email be at benfasigal AT gmail DOT com