Question

In an obtuse angled triangle, how many angles are obtuse.
​

Answer 1

Answer:

An obtuse triangle (or obtuse-angled triangle) is a triangle with one obtuse angle (greater than 90°) and two acute angles. Since a triangle's angles must sum to 180° in Euclidean geometry, no Euclidean triangle can have more than one obtuse angle.

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Answer 2

Answer:

A triangle can have a maximum of

1 obtuse angle.

Explanation:

Any triangle must have interior angles that add up to

180

∘

. An obtuse angle is an angle greater than

90

∘

but less than

180

∘

.

If you had an angle that was

91

∘

. The other

2

angles would have to be acute. This is because the other angles would take up

180

∘

−

91

∘

=

89

∘

of the triangle. Since

89

∘

is less than

90

∘

, this means the other

2

angles must both be acute. You are left with

1

obtuse angle.