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[molten birch]

Are we to take ABDC as a parallelogram? Because that's not indicated.

Hmm.

I think our first objective is to prove that ABDC is a parallelogram, else the question is maybe impossible.

Hmm.

Okay, let's think about it like this.

Is it possible - oh, yes, it is.

I was gonna ask "is it possible to have two different triangles with the given shared side length and opposite angle", but it very obviously is.

So yeah, no path forward unless we just assume ABC is congruent to BCD.

So it's a badly written question.

Okay, here's a thing we know is true; ABDC is a quadrilateral.

Thus, what is the sum of all internal angles of ABDC?

And we know it has two angles of 130 degrees, thus what is the sum of the other two angles?

Right.

Now, we have two sides and an obtuse angle for triangle BDC.

Which is actually enough to fully determine it, I think.

We would have to use the law of cosines to determine the third length.

...use... the law of cosines...

Stop.

Just do it, please.

Makes what impossible?

Which two angles?

Which "ones 'across' from 130"?

Name them.

Why would CBA and BCD sum to 100?

No they aren't. The other two angles in the parallelogram are ABD and DCA.

Use. Law of cosines. On triangle BDC. To find. The length. Of side CD.

Because. Then. We can use. Law of sines. To find. Angles. DBC. And DCB.

Actually, I'm not sure this approach is gonna work.

We don't learn anything about triangle ABC that we didn't already know, namely that angles ABC and BCA must sum to 50 degrees.

Also, what are you doing still measuring angles in degrees in a calculus course?

You used the word "calculus".

"Calculus final", you said.

Because, like I said, my confusion is with you measuring angles in degrees.

Okay, but your teacher is presenting angles in degrees. It doesn't matter, it's just that this is a habit you would break by the time you were, y'know, actually in calculus, because when you take actual calculus the difference begins to actually matter and it becomes obvious how much better radians are.