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Asked by Amy

Is the largest angle in a triangle a right angle? Explain your answer?

The largest angle in a generic triangle does not need to be a right angle. (eg for an equilateral triangle all angles are 180/3 = 60) However as above, IF a right angle is one of the angles in a given triangle then it must be the largest angle (as the sum of the 2 remaining angles must be equal to 90, and each angle must be greater than [and not equal to] 0). Also, it is obviously possible to have an angle larger than a right angle in a generic triangle (eg you could have an angle of slightly less than 180, and two extremely tiny angles just greater than 0), so again the largest angle in a GENERIC triangle need not be a right angle.

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Nick Gray
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The sum of all three angles in a triangle is 180°. So if the triangle has a right angle then it is the largest angle, as the sum of the other two must be 90°, hence they must be individually smaller than 90°. A triangle can have an angle larger than 90° though.

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Joseph John Fernandez
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