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) = 160o because it is double the angle.
Arc(CD) = arc(BC) because their chords are congruent. Therefore, arc(CD) = 160o.
This means arc(BD) = 360o - 160o - 160o = 40o.
Angle(x) is one-half the arc it intercepts, so it is 20o.