Which statement describes an equiangular triangle?

Which statement describes an equiangular triangle?

• A. It has exactly two obtuse angles.
• B. All sides are equal.
• C. All angles are equal.
• D. No sides are equal and no angles are equal.

Answer: (C)

Equiangular means all the interior angles are equal. In a triangle, that forces each angle to be 60 degrees because the three angles sum to 180 degrees. So the direct way to describe an equiangular triangle is that all angles are equal. Since equal angles imply equal opposite sides in a triangle, such a triangle is also equilateral. The other statements don’t fit: you can’t have two obtuse angles in a triangle, and saying no sides or angles are equal contradicts the idea of equal angles.

Equiangular means all the interior angles are equal. In a triangle, that forces each angle to be 60 degrees because the three angles sum to 180 degrees. So the direct way to describe an equiangular triangle is that all angles are equal. Since equal angles imply equal opposite sides in a triangle, such a triangle is also equilateral. The other statements don’t fit: you can’t have two obtuse angles in a triangle, and saying no sides or angles are equal contradicts the idea of equal angles.