Vertical angles between parallel lines and a transversal are equal. Angle [tex]\angle CED[/tex] has been proved to be [tex]30^o[/tex]
From the given figure:
[tex]\angle ABC[/tex] and [tex]\angle BED[/tex] are vertical angles
Using vertical angle theorem:
[tex]\angle ABC = \angle BED[/tex]
Also:
[tex]\angle BED = \angle BEC + \angle CED[/tex]
Make BEC the subject
[tex]\angle BEC= \angle BED - \angle CED[/tex]
Recall that: [tex]\angle ABC = \angle BED[/tex]
[tex]\angle BEC= \angle ABC - \angle CED[/tex]
Substitute known values
[tex]\angle CED = 70^o - 30^o[/tex]
[tex]\angle CED = 40^o[/tex]
Hence:
[tex]\angle CED[/tex] has been proved to be [tex]30^o[/tex]
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