Let us consider the situation when the axes are inclined at an angle omega . If the coordinates of a point P are (x_1,y_1),thenPN = x_1, PM =y_1where PM is parallel to the y-axis and PN is parallel to the Xaxis. The straight line through P that makes an angle thetawith the x-axisis RQ = y-y_1, PQ = x - x_1 " From " DeltaPQR, we have (PQ)/(sin(omega-theta))=(sqrtQR)/(sin theta) or y-y_1 = (sin theta)/(sin(omega-theta))(x-x_1) writen in the form of y-y_1=m(x-x_1) " where " m=(sin theta)/(sin(omega-theta))Therefore, if the slope of the line is m, then the angle of inclination of the line with the x-axis is given by an tan theta=((m sin omega)/(1+m cos omega)) The axes being inclined at an angle of 60^(@), the angle between the twostraight line y=2x+5 and 2y+x+7=0

Let us consider the situation when the axes are inclined at an angle o

1.	Let us consider the situation when the axes are inclined at an angle omega . If the coordinates of a point P are (x_1,y_1),thenPN = x_1, PM =y_1where PM is parallel to the y-axis and PN is parallel to the Xaxis. The straight line through P that makes an angle thetawith the x-axisis RQ = y-y_1, PQ = x - x_1 " From " DeltaPQR, we have (PQ)/(sin(omega-theta))=(sqrtQR)/(sin theta) or y-y_1 = (sin theta)/(sin(omega-theta))(x-x_1) writen in the form of y-y_1=m(x-x_1) " where " m=(sin theta)/(sin(omega-theta))Therefore, if the slope of the line is m, then the angle of inclination of the line with the x-axis is given by an tan theta=((m sin omega)/(1+m cos omega)) The axes being inclined at an angle of 60^(@), the angle between the twostraight line y=2x+5 and 2y+x+7=0
Answer» `90^(@)` `TAN^(-1)(5//3)` `tan^(-1)(sqrt3//2)` `tan^(-1)(5//sqrt3)` ANSWER :D