How many triangles exist with the given angle measures 55,45,90 degrees

A. Exactly one unique triangle exists with the given angle measures.

B. No triangle exists with the given angle measures.

C. More than one unique triangle exists with the given angle measures.

Answer: The correct answer is B.

The first thing to check is the sum of the angles. 32 + 51 + 97 = 180. Therefore, the sides equal 180 and we can have a triangle because all triangles have exactly 180 degrees.

Second, the number of triangles with these measures is endless. Imagine taking the initial triangle and doubling the size. The angles don't change but the triangle does. We could keep doubling the size forever.