Question

Under which angle conditions could a triangle exists?

Answer 1

A triangle has 3 sides and 3 angles.

It must have a sum of 180 degrees.

All angles must be positive.

If you're referring to a right triangle, one angle must be 90 degrees and the other two should equal 90 degrees.

If you're referring to an acute triangle, all three angles must be less than 90 degrees but must be equal to 180 degrees in the end.

If you're referring to an obtuse triangle, one triangle must be more than 90 degrees, and the total degree should be added up to 180.

Answer 2

an acute angle is <90 degrees

a right angle is equal to 90 degrees

an obtuse angle is >90 degrees

Any triangle has angles adding to 180 degrees

therefore three acute angles, eg. 60, 60 and 60 degrees can make up a triangle

2 acute angles and a right angle, say 45 and 45 degrees and 90 degrees make a triangle

any obtuse angle + a right angle will be larger than 180 degrees, so no triangle can exist. another acute angle will make the number of degrees even larger

any 2 obtuse angles will make a number larger than 180 degrees, so with an acute angle is impossible

2 acute and an obtuse angle is possible, say 40, 40 and 100 degrees