42°
Step-by-step explanation:
[tex]\angle BAE =180\degree -132\degree[/tex]
(Angles in linear pair)
[tex]\angle BAE =48\degree[/tex]
[tex]\angle AEB =90\degree..(\because \overrightarrow{EC}\perp\overrightarrow{ED})[/tex]
[tex]\angle ABE = 180\degree-(48\degree+90\degree)[/tex]
(Angle sum postulate of a triangle)
[tex]\implies\angle ABE = 180\degree-138\degree[/tex]
[tex]\implies\angle ABE = 42\degree[/tex]
[tex]\angle CDE =\angle ABE = 42\degree[/tex]
(corresponding angles)
[tex]\implies x\degree=\angle CDE[/tex]
(vertical angles)
[tex]\implies x\degree=42\degree[/tex]
[tex]\implies x=42[/tex]
