Construction of pentagon with all sides and alternative two angles given.

Question

All sides of a pentagon ABCDE are given. Angles A & C are given. Can such pentagon be created by straightedge and compass?

Answer 1

you have enough information given to construct the triangles $ \triangle BAE $ and $ \triangle BCD $ (Side Angle Side given) so you can construct the segments EB and BD,

Then first construct the triangle $ \triangle DBE $ (all sides given) and then "add" the triangles $ \triangle BAE %$ and $ \triangle BCD $ to them.

good luck

Answer 2

A hint: consider the triangles $EAB$ and $BCD$.

Second hint: The side lengths $|EA|$ and $|AB|$ together with the angle at $A$ allow the construction of the triangle $EAB$; in particular, the length of the diagonal $|BE|$ is determined.