Use the given conditions to determine the number of possible triangles.

Question

first angle measure: 40∘

second angle measure: 75∘

third angle measure: 65∘

Do the given conditions create a unique triangle, more than one triangle, or no triangle?

Responses

unique triangle
unique triangle

more than one triangle
more than one triangle

no triangle

Answer 1

To determine whether the given angles can form a triangle, we need to check if they satisfy the triangle sum property. The sum of the interior angles of a triangle must equal 180 degrees.

Let's add the given angles:

• First angle: 40°
• Second angle: 75°
• Third angle: 65°

Now summing them:

\( 40° + 75° + 65° = 180° \)

Since the sum of the angles is exactly 180°, these angles can indeed form a triangle.

Furthermore, since the measures of the angles are fixed and add up to 180°, this configuration creates a unique triangle.

The answer is:

unique triangle