definition of rectangle I am wondering whether it is fine to define a rectangle with right angles like Wikipedia's page of rectangle.

In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. It can also be defined as an equiangular quadrilateral.

Because that the sum of the angles of a quadrilateral is 360 degrees is a theorem, it is little ambiguous for me to define a rectangle with a theorem and some calculation (360/4=90).
And if that's is the case, is it fine to say a regular polygon (except equilaterial triangle) is a polygon which has equal sides and equal inner angles?  

well, you know that right angles exists (it's an axiom). So I think it make sense to state that if a figure having four right angles exists, then you call it rectangle. You just have to show that such a figure exists :-)
