Question

Can a triangle have two obtuse angles? Give reason for your answer.

Answer 1

We know, the sum of three angles of a triangle is equal to 180°.

Also, an obtuse angle is one whose value is greater than 90° but less than 180°.

If the triangle has two obtuse angles, then there are at least two angles which are 91° each.

On adding these two angles,

Sum of the two angles = 91° + 91°

⇒ Sum of the two angles = 182°

This already exceeds the sum of three angles of the triangle, even without considering the third angle.

Again, if we consider the case where one angle of the triangle is 90°, we have a right-angled triangle. The rest two angles must be less than 90° each so as to satisfy the property of a triangle, which states that the sum of the three angles of a triangle should be equal to 180°.

Thus, a triangle cannot have two obtuse angles.