7.e mode 360=1
=>(7*e)%360=1 (when 7* e will be mode with 360 reminder will be =1)
=>so multiple of 360 == 7*e and reminder 1(i.e)7.e must be 361, 721, 1081, 1441, etc Dividing each of these in turn by 7 to see which is divisible by 7, we find that 721/7 = 103,
hence e = 103.