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3 years ago

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

Mathematics

2 answers:

just olya [345]3 years ago

8 0

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

Komok [63]3 years ago

6 0

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

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