Question

If the sides of the triangle produced in order,prove that the sum if the exterior angle so formed 360

Answer 1

Answer:

In ABC , By Angle sum property of triangle,

ABC + BAC + BC A =180°-------(1)

Now, By linear pair property

1 + BAC = 180° ---------(2)

And 2 + ABC = 180° ---------(3)

And 3 + BCA = 180° ---------(4)Add equation (2) (3) and (4)

1 +BAC+2+ABC+3+BCA= 180°+180°+180°

1+2 +3 + BAC+ABC+BCA = 540°

1+2 +3 + 180° = 540° (from eq 1)

1+2 +3 = 540° - 180°

1+2 +3 = 360°

Hence, it is proved that sum exterior angle of triangle is 360°