Question

How many triangles exist with the given angle measures?

60°, 60°, 60°

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 1

The sum of the angles in a triangle is 180°, so the angles do form a triangle. Since two of the three angles are congruent, the triangle is an isosceles triangle. An infinite number of isosceles triangles exist with different side lengths. Therefore, more than one triangle exists with the given angle measures.