## Under which angle conditions could a triangle exist? Check all that apply.

Question

Under which angle conditions could a triangle exist? Check all that apply.

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1 week 2021-11-25T15:23:13+00:00 2 Answers 0 views 0

3 acute angles

2 acute angles, 1 right angle

2 acute angles, 1 obtuse angle

Step-by-step explanation:

The sum of the three angles in a triangle is always equal to .

Also we have:

– An acute angle is an angle measuring less that 90 degrees

– A right angle is an angle measuring exactly 90 degrees

– An obtuse angle is an angle measuring more than 90 degrees

Let’s now analyze the different statements:

– 3 acute angles  –> this is possible, since all the three angles measure less than 90 degrees, their sum can still be 180.

– 2 acute angles, 1 right angle  –> also possible: one angle measures 90 degrees, while the other two together have a sum of 90, so they should be both acute

– 1 acute angle, 1 right angle, 1 obtuse angle
–> not possible: the right angle is 90 degrees, the obtuse angle is more than 90 degrees, so their sum is already larger than 180

– 1 acute angle, 2 obtuse angles  –> not possible: the sum of 2 obtuse angles is more than 180 degrees

– 2 acute angles, 1 obtuse angle –> possible: the obtuse angle is more than 90 degrees, while the two acute angles are less than 90, so they can add together to form 180 degrees