What is the maximum possible number of obtuse angles in a triangle? Justify your answer. [3 MARKS]

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Solution

Answer: 1 Mark
Reason: 2 Marks

In a triangle, only one obtuse angle can exist.

If we have more than one obtuse angle in a triangle, then the sum of two (obtuse) angles will exceed $180^{\circ}$ .

But sum 3 angles of a triangle is $180^{\circ}$ .

$\Rightarrow$ A triangle can not have more than one obtuse angle.

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What is the maximum number of obtuse angles in a triangle?

Q. The maximum number of obtuse angles a triangle can have is 1.

Q. Is there any possibility that a triangle has two right angles? Justify your answer.

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What is the maximum possible number of obtuse angles in a triangle? Justify your answer. [3 MARKS]

Answer: 1 Mark Reason: 2 Marks In a triangle, only one obtuse angle can exist. If we have more than one obtuse angle in a triangle, then the sum of two (obtuse) angles will exceed 180∘. But sum 3 angles of a triangle is 180∘. ⇒ A triangle can not have more than one obtuse angle.