For a cw-complex the pair $\left(X,X^n \right)$ is n-connected

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Hello I am currently self-learning about (algebraic-)topology using Hatchers book.

My definition of $n$-connected is that $\pi_k\left(X,X^n\right)=0$ for all $1\le k \le n$.
I do know about the cellular approximation theorem but how can I apply it here ? Is there any trick to show that any representative is homotopic to something with image in $X^n$ using cellular approximation ?

Would appreciate any help