Let θ=(5x−12)∘, where x is a real number. Answer the following questions with complete justification:
a. (i) Write an algebraic expression for the angle that completes θ to a right angle.
b. (ii) Find the range of values of x for which both θ and the angle obtained in part (i) are acute angles.
c. (iii) Prove that, for every value of x found in part (ii), the two angles together form exactly a right angle.
d. (iv) Discuss whether θ possesses a completing angle if θ becomes obtuse. Support your answer with suitable inequalities.