It depends on what type of triangle it is.
If it is equilateral then it will also be equiangular.
If it is isosceles then it may be equiangular (it depends whether it is equilateral or not - an isosceles can be equilateral or it can just have two equal sides).
Any other type of triangle will not be equiangular.
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No, an equilateral triangle has to be equiangular, but an equiangular triangle does NOT have to be equilateral
No.
Every equilateral triangle is equiangular, and every equiangular triangle is equilateral.
No there is not. A right triangle has to have an angle of 90 degrees. An equiangular triangle has 3 equal angles. If a right triangle was equiangular, it would be 90 times 3 equaling 270 degrees. There are only 180 degrees in a triangle.
A triangle is equilateral if, and only if, it is equiangular. That is to say, the two statements are equivalent.