Question

Prove that if in a triangle one angle is obtuse the other two angles must be acute angles.

Answer 1

Answer:

In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°. Here, the triangle ABC is an obtuse triangle, as ∠A measures more than 90 degrees. ... Hence, if one angle of the triangle is obtuse, then the other two angles with always be acute.

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Answer 2

Answer:

If in a triangle one is obtuse (one of the interior angles is greater than 90°) than other two angles have to be acute (less than 90°) because The sum of the angles of a triangle in Euclidean geometry must be 180°

Step-by-step explanation:

Suppose a triangle ABC with angle a obtuse and angle b obtuse and angle c obtuse

Then

sum of angles of a triangle =angle a+ angle b+ angle c

180= (more than 90) +(more than 90) +(more than 90)

Which is not possible.

Hence if angle is obtuse and other two are acute then only euclidean geometry is correct.