State True/False.

A triangle is obtuse angled if one angle is greater than the sum of the other two angle.

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True

False

answer is A.

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Detailed Solution

It is given that one angle of a triangle is greater than the sum of the other two angle.
Here, we have to find whether the given triangle is obtuse angled or not.
Obtuse angles are those angles that lie between 90 degrees and 180 degrees.
Let ABC be the triangle, then according to question, we have,

∠ A > ∠ B + ∠ C

-------------(1)
We know that the sum of all the angles in a triangle is

180 °

∠ A + ∠ B + ∠ C = 180 ° ∠ B + ∠ C = 180 ° − ∠ A − − − − (2)

Substituting equation (2) in equation (1),

\Rightarrow ∠ A > 180 ° - ∠ A

Adding

∠ A

both sides,

\Rightarrow ∠ A + ∠ A > 180 ° - ∠ A + ∠ A

\Rightarrow 2 ∠ A > 180 °

\Rightarrow ∠ A > 90 °

∠ A > 90 °

it means

∠ A

is an obtuse angle.
Therefore, a triangle is obtuse angled if one angle is greater than the sum of the other two angle.
Thus, the given statement is true.
Hence, option (1) is correct.

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