How many triangles exist with the given angle measures? 32 degrees, 51 degrees, 97 degrees

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

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

C. No triangle exists with the given angle measures.

D. A triangle can be drawn with more than one acute angle.

Question

Ayana Cordova

Mathematics

6 June, 06:17

How many triangles exist with the given angle measures? 32 degrees, 51 degrees, 97 degrees

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

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

C. No triangle exists with the given angle measures.

D. A triangle can be drawn with more than one acute angle.

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Answers (1)

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Johns · Answer 1

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.