Q1:

Statement 1 is insufficient in itself. Reason- there can be 3 tollgates and it can distance between each of them can be more than 10 miles. But in case it have 4 gates or more than atleast 1 will have less than 10 miles gap.
(Also there can be only 2 tollgates in which case the distance is 25km)

When we combine stmt 1 & 2 we can conclude that atleast a pair of gates will be less than 10 miles.

Q2.

Let's assume angle QRS = a, Angle QRS = QSR as QR = QS
Again assume angle TUS = b, Angle TUS = SUT as TU = ST

now we can express Angle RQS = 180-2a, Angle STU = 180-2b

In triangle QPT:
All three angles must be 180.
=> (180-2a) + 90 + (180-2b) = 180
or solving it you get (a+b) = 135

IN quadrilateral RSUP,
Angle SRP = 180-a , Angle SUP = 180-b

Sum of angles of quadrilateral is 360.
=> 90+ (180-a)+(180-b)+x = 360
=> 90 + x = a +b
=> x = 135-90 = 45

nm, i get it... when i thought bout it in my head it seemed right but when i drew it out tollbooth @ 0 miles - tollbooth at 11 miles tollbooth at 22 miles... it made sense... wierd... wat a simple question 2 mess up on... Got carried away with the wrong thinking the whole time... this seems to happen alot, i think i need to be more focused...