Geometry

[Guest]

Any one can help how to find the X?

[nathi123]

Given that AD=DC ; DE [tex]\bot[/tex] [tex]AC \Rightarrow EA=CE \Rightarrow \angle EAC=\angle ECA=x; EA=BC=CE \Rightarrow \angle BEC=\angle CBE=y[/tex]
[tex]\triangle BCE\Rightarrow \angle BCE=180^\circ -2y ; \angle BEC=2x[/tex] because it is external to [tex]\triangle CEA; \angle BCA=75^\circ = x+180^\circ -2y[/tex]
[tex]\Rightarrow 75^\circ = x+180^\circ -4x \Leftrightarrow 3x=105^\circ \Leftrightarrow x=35^\circ[/tex]