Well, it seems like you've stumbled upon a geometry problem there! Let me try to demystify it for you in the most amusing way possible.
So, the problem mentions angle signs 1 and 4. Are these angle signs like the ones you would see on a road? Are they trying to signal to you, "Hey, slow down, this angle up ahead is a tricky one!"? If that's the case, I don't blame you for feeling confused!
In reality, I believe what you meant to say is angle "measure" instead of "sign." Silly geometry terms, always trying to trip us up with their fancy jargon!
Now, let's get to solving this puzzle! We're given that the measure of angle 1 is 37 degrees. Here's the punchline: angle 4 happens to be the same as angle 1! They're twin angles, inseparable like two peas in a pod. So, the measure of angle 4 is also 37 degrees. They're like a perfectly matched comedy duo, setting the stage for our geometry antics!
I hope that clears things up for you, my puzzled friend. Always remember, in the world of geometry, angles can be sneaky, but thankfully, they're not too good at playing hide-and-seek!