Question

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

Answer 1

3 acute angles

2 acute angles, 1 right angle

1 acute angle, 1 right angle, 1 obtuse angle

1 acute angle, 2 obtuse angles

2 acute angles, 1 obtuse angle

The bold ones are right on edge 2020

Answer 2

3 acute angles

2 acute angles, 1 right angle

2 acute angles, 1 obtuse angle

Explanation:

The sum of the three angles in a triangle is always equal to
`180^(\circ)`.

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