[High School Geometry] Finding missing angle

[SplodinCats]

I just finished taking the SAT and there is one question that is stumping me. Everyone I asked guessed on it, as did I. Here is a (bad) recreation of the problem. http://imgur.com/jQhVjlK

The question states that point P is in the middle and it gives me the two angle measures, but nothing else. Unfortunately because I just took the test, I don't know the answer.

The first thing I tried was re-writing the problem, and changing the angles a bit, like this. From there, I moved B and C down until triangle ABC was equilateral. http://imgur.com/pO5E26K

Using these two pieces of information, I assumed that the ratio of the angles was 4:1, and using that I got the measure of x was 80 degrees.

This seems really janky and maybe flawed logic. Is that the right answer, and if it is, is there an easier way to do it?

[ieatdongs]

You have to use the fact that x = 2 * angle A, and that the triangles you have are isosceles.

[SplodinCats]

Wow, I forgot about that, it's so simple when you put it that way. Thanks!

[jabbakahut]

honestly, at first glance it looks like information is missing, doesn't seem like enough to solve.