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Let me re-state the problem correctly

This is the 3rd and final question I post from the book, The Unsolvable and the Solvable.

It is NOT a homework question. This is something for everyone to try out for interest.

Consider an isoceles triangle ABC and an equilateral triangle BCF which share the side BC as shown below. Please ignore the dotted lines.

...........................A

...................D

......................................E

.............B_________________C

...........................F

D is a point on side AB and E is a point on side AC.

angle DAE=20 degrees

angle DEA=20 degrees

angle EDC=10 degrees

angle ECD=10 degrees

angle DBC=80 degrees

angle DCB=70 degrees

angle BDC=30 degrees

WITHOUT using the sine and cosine law, determine angle EFC.