Answer the following questions related to a circle.
a. (i) Define (a) an arc of a circle and (b) a central angle of a circle.
b. (ii) State the relationship between the measure of an arc and the measure of the central angle that subtends it.
c. (iii) In a circle with centre O, the measure of ∠AOB is 72∘. Find the measure of arc AB. Give reason for your answer.
d. (iv) In another circle, the measure of arc PQ is 135∘. What is the measure of ∠POQ? Give reason for your answer.