221k views
0 votes
Do the given conditions determine one unique triangle, many similar triangles, many nonidentical triangles or no triangle?

100°,70°,40°

2 Answers

5 votes

Final answer:

The given angles (100°, 70°, 40°) sum to 210°, exceeding the total sum of 180° required for a triangle's internal angles; thus, no triangle can be formed from these angles.

Step-by-step explanation:

The question asks about the possibility of forming a triangle given three angles: 100°, 70°, and 40°. As per the basic properties of a triangle, the sum of its internal angles must always equal 180°. The provided angles sum to 210°, which exceeds this requirement.

Therefore, these conditions do not determine a unique triangle, any similar triangles, or any nonidentical triangles since no triangle can exist with these angles. This is confirmed with a simple addition: 100° + 70° + 40° = 210°, which violates the triangle angle sum property.To determine whether the given conditions can form a triangle, we need to check if the sum of the angles is equal to 180 degrees. In this case, the given angles are 100°, 70°, and 40°.

Step 1: Add up the three angles: 100° + 70° + 40° = 210°.

Step 2: Since the sum of the angles is 210°, which is greater than 180°, the given conditions do not form a triangle.

In a triangle, the sum of the interior angles is always 180 degrees. If the sum exceeds 180 degrees, it means that the angles cannot form a triangle.

User Eric Cloninger
by
8.4k points
6 votes

No triangle

========

Sum of angles in a triangle is always 180 degrees.

Given angles are 100°, 70°, and 40°.

The sum of these angles is:

  • (100° + 70° + 40°) = 210°

This is greater than 180°, hence it is not possible to form a triangle with these angles.

User Marian Busoi
by
8.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.