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Triangle and Sum of Its Internal Angles

In triangle A...

Question

In triangle ABC, if ab is the greatest side then prove that angleC>60.

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Solution

AB is greatest side then AB>BC means
∠C > ∠A
and AB > AC means
∠C > ∠B

adding these,
2∠C > ∠A + ∠B
3∠C > ∠A + ∠B + ∠C
3∠C > 180°
∠C > 60°

hope it help

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