Question

if the sides of a triangle are produced in order ,prove that the sum of exterior angles so formed is 360 degree.

Answer 1

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

Answer:

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