Can a triangle have both an obtuse and a right angle? Explain and provide an example.
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It would violate the theorem of the sum of the interior angles of a triangle summing up to 180∘.
Explanation:
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.
Explanation:
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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