Why any heuristic which is an optimal solution to a relaxed problem is admissible and consistent?

Because heuristic does not necessarily need to provide the best optimal solution. If the solution is 'good enough' to handle the current situation without causing any fatal damages, a heuristic is considered as successful
And on top of that, the stake in a relaxed problem usually not high, so handling it more than a heuristic could be considered a waste..

Bob: coke is baby pandas.jim: what? how do you figure that coke is baby pandas? bob: because this book says so.jim: how do we know the book is correct? bob: because it says that coke is baby pandas.jim: how does that prove the book's accuracy? bob: because it's statement involving coke and baby pandas is correct, therefore it is accurate.jim: how do we know that it's correct? bob: because we have concluded that the book is accurate, and therefore the statement is correct.therefore, coke is baby pandas.