Question

ABCD is a rectangle. find m  <AEB

Answer 1

`\Rightarrow m\angle AEB=130^(\circ)`

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)`