The angle made by the perpendicular drawn from the origin to the line x+2y−25=0 with  X- axis is

The given equation is x+2y−25=0 To reduce the general equation of the line ax+by+c=0 in normal form, isolate the constant  term and then divide both sides with a2+b2 and make constant term must be positive. Hence, x+2y=25 Divide both sides with 12+22=5x5+2y5=2 By comparing the above equation with normal form of the line xcos⁡α+ysin⁡α=pIt implies cosα=15,sinα=25 Hence tan⁡α=2 Therefore, the angle required is α=tan−1⁡(2)