Question

show that the sum of exterior angle of trangle is 360.

Answer 1

Theorem: If any side of a triangle is extended, then the exterior angle so formed is the sum of the two opposite interior angles of the triangle.

Exterior Angle Property of a Triangle

In the given figure, the side BC of ∆ABC is extended. The exterior angle ∠ACD so formed is the sum of measures of ∠ABC and ∠CAB.

Proof: From figure 3, ∠ACB and ∠ACD forms a linear pair since they represent the adjacent angles on a straight line.

Thus, ∠ACB + ∠ACD = 180° ……….(2)

Also, from the angle sum property it follows that:

∠ACB + ∠BAC + ∠CBA = 180° ……….(3)

From equation (2) and (3) it follows that:

∠ACD = ∠BAC + ∠CBA

Answer 2

SALUT AMIS!!


We know that,


Exterior angle + adjacent interior angle = 180

And if the sides are takes as n then,

Sum of all interior angles + Sum of all exterior angles = n × 180

Sum of all exterior angles =n × 180 - Sum of all interior angles.

Sum of all exterior angles = n × 180 -(n -2)× 180

180 n - 180 n + 360

= 360

Hence proved that sum of all exterior angles is 360