Question

Show that sum of three exterior angles of a triangle is 360

Answer 1

Lets XYZ is a triangle, so

Consider ΔXYZ in which ∠X = 1, ∠Y= 2 and ∠Z= 3
Let the exterior angles of X, Y and Z be ∠x, ∠y and ∠z respectively.
Now sum of angles in a triangle is 180° so,
That is  ∠1 + ∠2 + ∠3 = 180°
From the figure, we have
∠1 + ∠x= 180°  [Linear pair]
∠2 + ∠y = 180°  [Linear pair]
∠3 + ∠z = 180°  [Linear pair]
Add the above three equations, we get
∠1 + ∠x + ∠2 + ∠y + ∠3 + ∠z = 180° + 180° + 180°  or, (∠1 + ∠2 + ∠3) + ∠x + ∠y + ∠z = 540°
or, 180°+ ∠x+ ∠y + ∠z = 540°
or, ∠x + ∠y+ ∠z= 540° – 180° = 360°
Thus sum of exterior angles of a triangle is 360°.