In the given figure, MN = RM = RP, then what is the value (in degrees) of ∠MPR? 

In $$\triangle$$ RPN, using exterior angle property,

=> $$\angle$$ PRS = $$\angle$$ RPN + $$\angle$$ PNR

=> $$x+y=102^\circ$$ ----------(i)

Also, in $$\triangle$$ MRN,

=> $$\angle$$ MRN + $$\angle$$ MNR + $$\angle$$ RMN = $$180^\circ$$

=> $$\angle$$ RMN = $$(180-2y)^\circ$$

At point M, $$\angle$$ RMP + $$\angle$$ RMN = $$180^\circ$$

=> $$x+(180-2y)=180$$

=> $$x=2y$$ -----------(ii)

Substituting above value in equation (i),

=> $$2y+y=102^\circ$$

=> $$y=\frac{102}{3}=34^\circ$$

Substituting it in equation (ii), => $$x=2\times34=68^\circ$$

=> Ans - (B)