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State True/False.

Three obtuse angles are impossible in a triangle.

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True

False

answer is A.

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Detailed Solution

Here, we have to find whether there can be three obtuse angles in a triangle or not.
Obtuse angles are those that have a measure more than

90 °

but less than

180 °

.
Sum of the angles of the triangle are always

180 °

.
A triangle cannot have three obtuse angles.
For example:
Let’s assume that the three angles of a triangle are

110 °, 100 °, and 120 °

respectively in which all are obtuse angles.
By angle sum property of a triangle, the sum of all the angles should be

180 °

⇒ 110 ° + 100 ° + 120 ° ⇒ 330 °

As we can see that, the sum of all the angles is not

180 °

.
Therefore, it is not possible for a triangle to have more than one obtuse angle as the sum of all the angles of a triangle should always be

180 °

.
Therefore, 3 obtuse angles are impossible in a triangle.
Thus, the given statement is true.
Hence, option (1) is correct.

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