Why can't a triangle have a right angle and an obtuse angle?

Answer 1

It would violate the theorem of the sum of the interior angles of a triangle summing up to #180^@#.

We know that sum of all interior angles of a triangle is #180^@#. ---(1) If we assume that one angle is right angle of #90^@# and other angle be obtuse angle of #x# such that #x>90^@# . Sum of the 2 angles is then #90 + x >180^@#. It cannot be possible due to equation (1). (Contradiction). Therefore our initial assumption of #x>90^@# is incorrect and so the statement is false by the method of indirect proof.
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Answer 2

A triangle cannot have both a right angle and an obtuse angle because the sum of the angles in any triangle is always 180 degrees. If a triangle has a right angle (90 degrees), the other two angles must add up to 90 degrees to satisfy this rule, making them both acute angles (less than 90 degrees). Conversely, if a triangle has an obtuse angle (greater than 90 degrees), the other two angles combined would not be able to make up the remaining 90 degrees needed to reach a total of 180 degrees. Therefore, a triangle cannot simultaneously have a right angle and an obtuse angle.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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