Activation energy is the difference in the energy level of the reactants and the peak in the potential energy diagram (the energy of the transition state).
For an endothermic reaction, the products will be closer in energy to the transition state than what the reactans will be; so, the activation energy of the reversed reaction is lower than the activation energy of the forward reaction.
Activation energy of reverse and forward reactions is related by:
Activation energy of reverse rxn = Activation energy of forward rxn – ΔH rxn
=> Activiation energy of reverse rxn = 102 kJ/mol – 55 kJ/mol = 47 kJ/mol
Answer: 47 kJ/mol