Lines AB and CD intersect at point O. The measures of two opposite angles at O are given by ∠AOC=(3x+10)∘ and ∠BOD=(5x−50)∘.
a. (i) Form an algebraic equation in x using the relationship between the given angles.
b. (ii) Solve for x and hence find the measure of each of the four angles formed at O.
c. (iii) State whether ∠AOC is acute, right, obtuse or reflex, giving reason for your answer.