If you're using your performance on this, or any one problem, to determine your ability to succeed at getting a math degree, you're a fucking moron. If you can't do a problem, you look up an answer, study the fuck out of it until you understand how to get there and can replicate it yourself, then you pocket that information and move on. If you want to pursue a math degree, or anything of substance whatsoever, you're going to face a metric fuckton of problems. And big surprise, you're not going to know how to do every single one of them. You're gonna have your shortcomings and you either let those overwhelm you, or you learn from them and become a better person for it. Are you prepared & capable enough to gamble 50k on a degree right now? I don't know, that's for you to decide. But you're also not actually making that gamble right now; you have time. If you're not ready, stop sulking over a problem you couldn't solve and start studying.
You couldn't do a basic geometry problem. Awesome, that puts you in the same boat as the vast majority of math majors. Most modern curricula are, for better or for worse, severely lacking in rigorous material on Euclidean geometry. Problems like these are notoriously hard, not because they're genuinely hard problems, but because people aren't taught the tools needed to solve them. I have a math degree, it was a breeze to get, and I couldn't solve this. Unless you pursue research in something that directly uses Euclidean geometry, chances are very high that you can enroll in and complete a math degree, then go out into the real world and succeed in whatever job you do, without ever being able to solve a problem like this. Don't let one problem keep you from doing what you want to do with yourself, that's top tier brainlet shit right there.