Question

Is it possible to have a triangle such that none of the exterior angles is obtuse? Please help and explain

Answer 1

Answer: No, it is not possible

A triangle can only have 1 obtuse interior angle, leaving the exterior angle next to it to be acute. For example, if you have an interior angle of 120 (obtuse) then the adjacent exterior angle is 60 (acute)

The other two interior angles must be acute if you go with 1 obtuse angle, which leaves the corresponding exterior angles to be obtuse. If you wanted the exterior angles to be all acute, then you would need 3 obtuse interior angles, but that is not possible.

Why isn't it possible to have 3 obtuse angles? Consider a triangle with interior angles A, B, C. The three angles must add to 180

A+B+C = 180

If A,B,C were all larger than 90, then

A > 90

B > 90

C > 90

A+B+C > 90+90+90

A+B+C > 270

but that contradicts A+B+C being equal to 180