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

Question

first angle measure: 90∘

second angle measure: 75∘

third angle measure: 30∘

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

Responses

no triangle
no triangle

unique triangle
unique triangle

more than one triangle

Answer 1

To determine the number of possible triangles given the angles 90°, 75°, and 30°, we can use the fact that the sum of the angles in any triangle must equal 180°.

First, let's check the sum of the angles:

• First angle: 90°
• Second angle: 75°
• Third angle: 30°

Calculating the sum:

\[ 90° + 75° + 30° = 195° \]

Since the sum of these angles equals 195°, which exceeds 180°, these angles cannot form a triangle.

Thus, the conclusion is:

no triangle