Unfortunately without an exact reproduction of your project this will be really hard to pin point, but looking at what is given in the screen shot and prior experience with similar issues, I think this could be an issue with your package.json. Newer versions of node and npm look for the carets symbol (^) in both your package.json and the installed modules' package.json. When found, it will install newer versions of the package without error. Then when you go to run the project, the typings will break and Angular will refuse to compile and you get errors like these.
I would recommend removing all carets in older Angular projects to prevent this from happening as it is common occurence even when upgrading from more modern versions (I had this happen to me when upgrading from Angular 13 to Angular 14). However, with Angular 1.7/AngularJS not being supported anymore, I would recommend that you look into upgrading or rewriting the project in a modern version of Angular or another modern framework that fits the projects needs.