Mathematics

Problem

A straight jogging track

EF

intersects two straight walkways

AB

and

CD

at points

P

and

Q

respectively. The acute angle between

EF

and

AB

that lies inside the region between

AB

and

CD

68^\circ

. The angle on the opposite side of

EF

Q

that also lies inside the region between

AB

and

CD

(2y + 4)^\circ

. a. (i) If the two walkways

AB

and

CD

are required to be parallel for safety reasons, form an equation in

y

and find its value. b. (ii) For the value of

y

obtained in part (i), calculate the magnitude of the angle at

Q

. c. (iii) If instead

y = 30

, determine whether

AB

and

CD

would be parallel. Give a reason for your answer.