Question

prove that a right-angled triangle can never be a regular poygon

Answer 1

A right-angled triangle never can be a regular polygon because, its all the angles are not equal, if it would be a regular polygon then, the measurement of its all angle would be 60 degree(as it is a triangle, so, measurement of each equal angle = (n-2)*180 degree {n= number of sides}) but, here one angle is 90 degree and the others angle can't be be 90 degree because, the sum of the angles of a triangle is 180 degree. So, it is  not a regular polygon.