Angles

Given that \(AOB\) and \(COD\) are straight lines. Find the values of \(x\) and \(y\) in each of the figures below, stating your reasons clearly.

1. In the figure, the two straight lines intersect at point \(O\). Ray \(OE\) is drawn such that \(\angle AOE = x^\circ\) and \(\angle EOD = x^\circ\). The remaining angles are \(\angle DOB = y^\circ\) and \(\angle COB = 150^\circ\).
   
2. In the figure, the two straight lines intersect at point \(O\). Ray \(OE\) is drawn such that \(\angle AOE = 2x^\circ\) and \(\angle EOC = x^\circ\). The remaining angles are \(\angle COB = 114^\circ\) and \(\angle BOD = y^\circ\).