When we have to determine the angle at which two lines intercept, the ONLY thing we have to know is the slope of each line .
Once we have those, we are able to determine the length of the angles at the point of intersection. Those angles are fixed and do not change, hence A is ans
My qustion from experts is the if we were asked the measure of the angle, how to find that

[email protected] wrote:If lines y=mx+b and x=y+bm intersect at a degrees angle (where a<90 ), what is the value of angle a ?

(1) m=2

(2) m=b

y = mx + b_________________(1)
x = y + bm
y = x - bm_________________(2)

Slope of line (2) = 1 => the line is at 45 degrees with respect to the horizontal axis.
Slope of line (1) = m

Statement 1: m = 2
Slope of line (1) can be found out. So the angle between the 2 lines can be found out.
Sufficient.

Statement 2: m = b
Slope of line (1) is unknown. Hence angle between the lines is unkown.
Not sufficient.

Choose A