Question

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

Answer 1

Sum of all interior angles of a triangle equal to 180°
i.e
Angle ABC+ACB+BAC= 180° ---------1

Using exterior angle property of a triangle
ACD= ABC+ BAC ---------2
BAE= ABC+ACB ---------3
CBF= BAC+ ACB ---------4

Adding 1

ACD+BAE+CBF
= ABC+BAC+ACB+ABC+BAC+ACB
=2ABC+2BAC+2ACB
=2(ABC+BAC+ACB)
Using 1
ACD+BAE+CBF = 2(180°)
ACD+BAE+CBF=360°

Therefore, if the sides of a triangle are produced in an order, then the sum of the exterior angles are 360°.