Polygons - Properties of Special Quadrilaterals

A folding frame contains rhombus \(ABCD\). Side \(AD\) is extended beyond \(D\) to \(E\), and a supporting rod \(CE\) is fitted so that \(CD=CE\).
A handle \(ET\) is perpendicular to \(AE\). Ray \(EC\) lies inside the right angle \(DET\), as shown.
It is given that \[\angle ABC=122^\circ.\]

Find the following angles, giving reasons for your answers.

1. \(\angle ADC\).

   [1]

2. \(\angle DCE\).

   [3]

3. \(\angle CET\).

   [2]