Answer:
[tex]\Rightarrow m\angle AEB=130^{\circ}[/tex]
Step-by-step explanation:
As ABCD is a rectangle. So each angle of the rectangle is 90° and [tex]m\angle EAD=65^{\circ}[/tex], so
[tex]m\angle EAB=90^{\circ}-65^{\circ}=25^{\circ}[/tex]
The diagonals of the rectangle bisects each other. Hence,
[tex]\Rightarrow AE=BE[/tex]
In a triangle if two sides are equal then the angles opposite them will be equal.
So in triangle AEB,
[tex]m\angle EBA=m\angle EAB=25^{\circ}[/tex]
As the sum of the angles in a triangle adds up to 180°, so
[tex]\Rightarrow m\angle EBA+m\angle EAB+m\angle AEB=180^{\circ}[/tex]
[tex]\Rightarrow m\angle AEB=180^{\circ}- m\angle EBA-m\angle EAB[/tex]
[tex]\Rightarrow m\angle AEB=180^{\circ}-25^{\circ}-25^{\circ}=130^{\circ}[/tex]
