Triangle inequality

GRE Quant Problem Solving
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Sum of any two sides of a triangle must be greater than the third side, right?

The answer is correct, but the explanation given is wrong imo.

It must be a 2-89-89 triangle

Edit: The explanation given by Greg is correct. I had confused the angles with sides.

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And why exactly?

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Sorry, my bad. I’m talking about sides in my post, whereas we’re working with angles actually. The explanation Greg gave was correct.