Taking the period of day light on a certain day to be from 5.30a.m to…

Explanation

Period of day light is from 5.30 to 7.00p.m - 13hrs 30min. interval

24hrs make 1 day

∴ period of darkness = 24hrs - 13hrs 30mins = 10hrs 30mins.

Angle of sector of daylight = \(\frac{13 \times 60 + 30 \times 360}{(24 \times 60)}\)

= \(\frac{810}{1440}\) x 360^o

= \(\frac{291600}{1440}\)

= 202.5^o

202.5^o = 202.30^o

darkness period = 360^o - 202^o 30'

= 157^o30'

= 202^o30' 157^o 30'