“Oh no, it’s New Year’s today, and I haven’t decorated anything yet! What should I do?”

“No need to panic. How about making some Origami with paper?”

“I don’t know how to make Origami. Can you make one for me?”

Parthib brought a sheet of paper.

“Look, I’ve got a square piece of paper, $ABCD$, where $AB=BC=CD$, but $AC  \neq BD$. I’ve folded it along the diagonals, and they intersect at $E$. What’s cool is that $AE=DE$. While I’m folding this, can you figure out what the value of $\angle BAD + \angle ADC$ is?"