TITLE: What is the value of $\angle x$
QUESTION [2 upvotes]: Can any one help with this problem:what is value of $\angle x$

REPLY [1 votes]: The answer is $30^\circ$. 
Proof: Let this big triangle be $ABC$ where $$\angle ABC=20^\circ+60^\circ, \angle ACB=30^\circ+50^\circ, \angle BAC=20^\circ.$$
Also, let $D,E$ be the inner point on $AC, AB$ respectively.
Now, take a point $F$ on $AB$ such that $BD=BF$. Also, take a point $G$ on $DF$ such that $AD=AG.$ (Note that $G$ is outside of $ABC$)
Also, prove that the triangles $AGF, DBC$ are congruent. Then finally prove that $FD=FE$.
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