Question

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

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

Answer 1

Triangles exist:
3 acute angles 2 acute angles, 1 right angle
2 acute angles, 1 obtuse angle

Triangles DON'T exist for:
1 acute angle, 1 right angle, 1 obtuse angle
1 acute angle, 2 obtuse angles

Answer 2

1. 3 acute angles
2. 2 acute angles, 1 right angle
3. 2 acute angles, 1 obtuse angle

Explanation:

We have to check under which condition a triangle will exist.

• According to angle sum property of the triangle, the sum of all the three angles of a triangle is 180 degrees.

• An acute angle is an angle with a a measure less than 90 degrees

• A right angle is an angle with a measure of 90 degrees.

• An obtuse angle is an angle with a measure of greater than 90 degrees.

1. It is possible to have triangle with three acute angle

Example: A triangle with all the three angles of 60 degrees

2. It is possible to have a triangle with 2 acute angles and 1 right angle.

Example: A triangle with all the two angles of 45 degrees and one right angle.

3. It is not possible to have a triangle with 1 acute angle, 1 right angle and 1 obtuse angle. It will violate the angle sum property of triangle.

4. It is not possible to have a triangle with 1 acute angle and 2 obtuse angles. It will violate the angle sum property of triangle.

5. It is possible to have a triangle with 2 acute angles and 1 obtuse angle.

Example: A triangle with all the angles of 45 degrees, 40 degrees and 95 degrees