Under which angle conditions could a triangle exist? Check all that apply. 3 acute angles D 2 acute angles, 1 right angle 1 acute angle, 1 right angle, 1 obtuse angle D 1 acute angle, 2 obtuse angles 2 acute angles, 1 obtuse angle

## Step 1<br />A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. The sum of the interior angles of a triangle is always 180 degrees.<br /><br />## Step 2<br />Let's evaluate each option:<br /><br />### Option A: 3 acute angles<br />An acute angle is an angle that measures less than 90 degrees. If a triangle has three acute angles, each of these angles will be less than 90 degrees. The sum of these angles will still be 180 degrees, which is the sum of the interior angles of a triangle. Therefore, this option is possible.<br /><br />### Option B: 2 acute angles, 1 right angle<br />A right angle is an angle that measures exactly 90 degrees. If a triangle has one right angle and two acute angles, the sum of these angles will still be 180 degrees. Therefore, this option is also possible.<br /><br />### Option C: 1 acute angle, 1 right angle, 1 obtuse angle<br />An obtuse angle is an angle that measures more than 90 degrees. If a triangle has one acute angle, one right angle, and one obtuse angle, the sum of these angles will still be 180 degrees. Therefore, this option is also possible.<br /><br />### Option D: 1 acute angle, 2 obtuse angles<br />If a triangle has two obtuse angles, the sum of these angles will be more than 180 degrees. This is because each obtuse angle is more than 90 degrees. Therefore, this option is not possible.<br /><br />### Option E: 2 acute angles, 1 obtuse angle<br />If a triangle has one obtuse angle and two acute angles, the sum of these angles will still be 180 degrees. Therefore, this option is also possible.