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how do you find a chemical shift of an unknown arene?

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You would need the structure to estimate a chemical shift, or vice versa.  An aryl hydrogen would show a C-H peak in an IR spectrum just after 3030 cm-1 and C=C peak around 1500-1600.  HNMR and CNMR chemical shifts can vary a good deal depending on the structure.
Are you doing IR spect? 
 
In spect, you need to check the absorption charts and look to see if there are absorptions in the fingerprint region.