The graph of sec(x) is usually given in radians.
165 degrees is about 0.916Pi.
That is almost pi, so, as an approximation, you can read the value of the function for pi. This is valid because the graph is pretty flat around pi.
Ther you can read an approximate value of -1.
So your estimate can be -1.
Compare that estimate with the value when you use the calculator: it is sec(165 degrees) = -1.035, so I would say that our estimate is very good.
