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Polyester shirts come in knits and weaves, and in all kinds of styles. One thing they all have in common, regrettably, is the tendency to snag on just about any sharp object in your environment. If your polyester shirt has sustained a small snag, you might be tempted to just cut the snag off and be done with it. Don't give in to the temptation, though. Cutting off a snag can lead to large holes in your shirt. Use one of a few tried-and-true tricks for getting rid of polyester snags and you'll have smooth shirt fabric once again.
Grasp the fabric on either side of the snag. Pull the fabric from side to side, keeping the snag in the center. If you pull on the fabric with the thread that is snagged, the snag should ease itself back into the body of your shirt.
Push a snag tool from the back of the shirt to the front, right next to the snag. A snag tool is a needle with a rough end. The rough part of the snag tool will grab onto the fibers in the snag. Pull the tool back through the shirt and the snag will pull to the inside.
Remove larger snags and pulls with a needle and thread. Thread the needle with ordinary sewing thread. Push the needle from the inside of the shirt to the outside right next to the snag. Pull the thread over the snag, then push the needle back down through the same hole it came up. The thread will capture the snag loop and pull it through to the inside of the shirt. Tie the snag into a knot or attach it to the inside of the shirt with a dab of clear nail polish. This will prevent it from coming back to the front of your shirt.