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This is the last one I post from this book. It is pretty challenging.

Once again, it is NOT a homework problem.

Consider an isoceles triangle ABC and an equilateral triangle BCD which share the side BC as shown below. IGNORE the dotted lines in the diagram.

.....A

.....D

.......E

.....B_______________C

......D

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 the cosine law, determine angle EDC