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Ammonia is a polar molecule because the different electronegativity's of the nitrogen and the hydrogen molecules makes the hydrogen slightly positive and the nitrogen slightly negative. However there are 2 valance electons of the nitrogen atom which are not bonded to anything, which are called lone pairs.

The lone pairs means that the ammonia molecule is not symmetrical therefore the electronegativity's do not cancel eachother, creating a polar molecule.

( The reason why the shape is no longer symmetircal is because lone pairs repel more than the bond pairs of the N-H, and essentially the bonding pairs are "squeezed" together, which accounts for the smaller than expected bond angle of 107 degrees)

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