Answer:
- 3 acute angles
- 2 acute angles, 1 right angle
- 2 acute angles, 1 obtuse angle
Step-by-step 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
