Question

Prove that sum of the exterior angle of a triangle is 360o.

Answer 1

ANSWER:
Consider ΔABC in which ∠A = 1, ∠B = 2 and ∠C = 3
Let the exterior angles of A, B and C be ∠a, ∠b and ∠c respectively.
Recall that sum of angles in a triangle is 180°
That is ∠1 + ∠2 + ∠3 = 180°
From the figure, we have
∠1 + ∠a = 180° [Linear pair]
∠2 + ∠b = 180° [Linear pair]
∠3 + ∠c = 180° [Linear pair]
Add the above three equations, we get
∠1 + ∠a + ∠2 + ∠b + ∠3 + ∠c = 180° + 180° + 180°
⇒ (∠1 + ∠2 + ∠3) + ∠a + ∠b + ∠c = 540°
⇒ 180°+ ∠a + ∠b + ∠c = 540°
⇒ ∠a + ∠b + ∠c = 540° – 180° = 360°
Thus sum of exterior angles of a triangle is 360°

Answer 2

Let ABC be a triangle

Produce A to D, B to E & C to F

angle D = angle B + C

angle E = angle C + A

angle F = angle A + B

As we know,

angle A + B + C = 180

Therefore, angle A + B + C + A + B + C = 180 * 2

angle A + B + C + A + B + C = 360

Putting value of (A + B), (B + C), (C + A)

angle F + D + E = 360

Hence, sum of all exterior angles of a triangle is equal to 360