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