Question

if the sides of a triangle are produced in order,prove that the sum of the exterior angles so formed is 360°.

Answer 1

In a triangle when sides are produced,
Exterior angle and interior angle are supplementary to each other.
There are three sets of the angles
3(exterior angle+interior angle)=3(180)
Sum of the exterior angles + sum of interior angles =540
Sum of exterior angles =540-180
Sum of exterior angles =360.

Answer 2

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°