please see diagram

Let's finish labelling the vertices of the triangle:  let C be the vertex at angle(x) and let D be the upper vertex.

 

Arc(BC) = 160^o because it is double the angle.

 

Arc(CD) = arc(BC) because their chords are congruent. Therefore, arc(CD) = 160^o.

 

This means arc(BD) = 360^o - 160^o - 160^o = 40^o.

 

Angle(x) is one-half the arc it intercepts, so it is 20^o.