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34 E4b) Prove that the sum of the exterior aAABC is 360°(21 +22+3360°). |
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Answer» Consider ΔABC in which ∠A = 1, ∠B = 2 and ∠C = 3Let 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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