The sides BC, CA and AB of Triangle ABC, are produced in order, forming exterior angles /_ACD, /_BAE and /_CBF.  Show that

angle ACD + angle BAE + angle CBF = 360 degree.

To prove: ∠ACD + ∠BAE + ∠CBF = 360°

We know that, the exterior angle is equal to the sum of its interior opposite angles.

∴ ∠ACD = ∠1 + ∠2  .....(1)

∠BAE = ∠2 + ∠3  .....(2)

and ∠CBF = ∠1 + ∠3  .....(3)

Adding (1), (2) and (3), we get

∠ACD + ∠BAE + ∠CBF = 2(∠1 + ∠2 +∠3) 

 = 2 × 180°  [ Sum of angles of a triangle is 180°]

 = 360°