In most cases, the broken arm may be caused by the missing of screws. A replacement screw will fix the problem. You may go to the local optical store and ask the workers to fix the right screw for your frames. If the screw on your frames become loose, you can use a screw driver to tighten it. If the arms of your frame is broken off, you may repair broken frames at the temples by using hot glue (for plastic frames) - boiling water and pins. Alternatively, replace the temple piece with a piece from another set of glasses. Unscrew the hinges and screw the new temple piece into position.
You could try glue but chances are that it wall fall off again as you take them on or off. The other option is sticky tape, bandage the two bits together. It looks terrible cosmetically, but will hold it together.
You have very few options if you are not willing to buy a new pair and the optical department cannot fix it.
In some cases, the arms of the glasses frames can simply break away. This is totally common, but it's not advised to simply go out and purchase brand new frames. Instead, you can easily begin preparing the broken glasses frames by scraping away any paint or old glue around the area that you will reattach. Once you've prepared the site of the break, dab a
moderate amount of Krazy Glue to the end of the arm and reattach it to the frames. Krazy Glue tends to dry insanely quick, so be extra careful when applying the glue and trying to fix broken glasses frames. Just make sure to allow the broken glasses frames to dry for approximately a half a minute to a full minute.
In order to help with this problem, I find a detailed post for you. You can get more details and the solution is very great. You can check out https://www.johnfixesstuff.com/2015/02/how-to-repair-glasses-with-broken-arm.html Hope this helpful.
Personally, it is impossible to repair a pair of broken arm in glasses unless you replace it by a new arm. In common, the eyeglasses usually made of metal frame or plastic frame. If it broken, it is impossible to repair it. And you'd better buy a new pair or a new eyeglasses arm. But if the screw lose, you can tighten it. if there something broken in the connection part between front frame and arm, you can use wire to connect it again.