If a clock started at noon, then the angle traversed by the hour hand at 5.45 Pm will be:

Answer: (4)  172.5^o

Explanation:-
Angle traced by hour hand in 12 hrs = 360^o

Therefore, angle traced by hour hand in 5 hours 45 minutes = 23/4 hrs

= 360 x 23 / 12 x 4
= 30 x 23/4
= 15 x 23/2
= 345/2
= 172.5^o

Then, the angle traversed by hour hand at 5.45 PM will be  172.5^o.

Hence, the answer is (4)  172.5^o.