Question

Show the external angles of a triangle are 360 degrees

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°.

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