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Because there is a permanent dipole between the Br and Cl atom. The Cl atom has a higher electronegativity, so it will tend to pull the "shared" electrons formed in the bond to its pole, creating a permanent dipole and partial electron deficiency on the bromine atom.
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The electronegativity value of Br and Cl is 2.8 and 3.0 respectively.  

The electrinegativity difference in the Br-Cl bond is 3.0 – 2.8 = 0.2

If the electronegativity difference is below 0.5 the covalent bind is nonpolar

If the electronegativity difference is between 0.5 and 2.0 the covalent bond is polar.

If the electronegativity difference is above 2.0 the bond is ionic  

As the electronegativity difference is below 0.5 the Br-Cl covalent bond is nonpolar

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