AB is parallel to CD.
a) Find the value of angle x.
b) Work out the value of angle y.

C=2πr

C=2π6

C=37.6991118431

That's the arc length of the whole circle, i.e. the arc length of 360°.

65° is 18.055555555555555555555555555556% of 360°, (65/360*100)
so 18.055555555555555555555555555556% of 37.6991118431 is 
6.8067840827819444444444444444444.  Rounded to the nearest hundredth, the answer is 6.81 inches.

That's real pi, lets see if it makes a difference to use "stupid pi".

C=2πr

C=2π6

C=37.68

That's the arc length of the whole circle, i.e. the arc length of 360°.

65° is 18.055555555555555555555555555556% of 360°, (65/360*100)
so 18.055555555555555555555555555556% of 37.68 is 
6.803333333333333333333333.  Rounded to the nearest hundredth, the answer is 6.80 inches.
Yep makes a difference.  That's why you don't use stupid pi.  3.14159 is what we always used in engineering, or just the pi button and using a ton of digits.

6.80 inches.