Answer:
80°
Step-by-step explanation:
We have redrawn the figure with nomenclature.
Given,
∠C = 45°
∠D = 55°
We have to find the value of x.
Solution,
In ΔCDE
[tex]\angle C = 45\°\\\\ \angle D = 55\°[/tex]
Now according to angle sum property;
Sum of all the angles of a triangle is equal to 180°.
framing in equation form, we get;
[tex]\angle C+\angle D+\angle E =180\°[/tex]
On substituting the given values, we get;
[tex]45+55+y=180\°\\\\100+y=180\°\\\\y=180\°-100\°\\\\y =80\°[/tex]
Now In Δ AEB and Δ CED
[tex]m \angle AEB =m\angle CED[/tex] ⇒ (Vertically opposite angles.)
Now [tex]m\angle CED = y\°= 80\°[/tex]
So [tex]m\angle AEB =x\°= 80\°[/tex]
Hence [tex]x =80\°[/tex].
