We know that the sum of the angles of a triangle is 180º.
The given angles are 53°, 64° and 63°.
Sum of the given angles = 53° + 64° + 63° = 180º
Here, the sum of the angles of the triangle is 180º. But, the measure of sides of the triangles is not known. So, infinitely many triangles can be drawn and sum of the angles of every triangle is 180º.
The number of triangles that can be drawn the measure of whose angles are 53°, 64° and 63°, is __infinite many__.