Question

Show that the Sum of the exterior angle of triangle is equal to four right angle

Answer 1

Consider a Triangle ABC.

In Triangle ABC ,

Exterior angle A = angle B + angle C

Exterior angle B = angle A + angle C

Exterior angle C = angle A + angle B

Therefore ,

→Ext. angle A + Ext. angle B + Ext. angle C
= B+C+A+C+A+B

→Ext. angle A + Ext. angle B + Ext. angle C
= 2(A+B+C)

[ In a Triangle Sum of all three angles is 180°]

→ Ext. angle A + Ext. angle B + Ext. angle C
= 2(180)
=360°

Therefore , Sum of exterior angles of Triangle = 360° = sum of four right angles.
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