In the adjoining figure, find the measure of angle FEB, if the lengths of sides AD, DF and FE are equal and `angleACB=65^(@)`.

Explanation

We kanow that in `DeltaABC`,
`angleA+angleB+angleC=180^(@)` (angle sum property)
`implies" "angleA=180^(@)-90^(@)-65^(@)=25^(@)`
since, `AD=DF` (given)
`implies" "angleDFA=angleDAF" "( :'" angles opposite to equal sides are equal")`
`=25^(@)`
`:. angleADF=180^(@)-(25^(@)+25^(@))`
`=130^(@)`
`implies" "angleFDE=180^(@)-130^(@)=50^(@)` (linear pair axiom)
But since `FD=FE` (given)
`:. angleFED= angleFDE` (angles opposite to equal sides are equal)
`=50^(@)`
`:. angleFEB=180^(@)-angleFED` (L.P.A.)
`=180^(@)-50^(@)`
`=130^(@)`