ONLY options B and F are correct
For line r to be perpendicular to line p, then the angle between them must be equal to 90 degrees
We shall be considering the validity of the options one after the other
a) measure of angle 2 is 90
This is not correct for us to conclude. This is because angle 2 is between the lines n and p
So if angle 2 is 90, then it serves to show that lines n and p are perpendicular and not lines r and p
b) measure of angle 6 is 90
This is correct and sufficient enough for us to conclude. As we can see, the angle is between r and p and this is enough a reason for the two to be perpendicular
c) measure of angle 6 is equal measure of angle 3
This is not correct and sufficient on its own. It can only be correct when we have the specific value of either angle as both are equal in value. So a specific measure would ensure our validation that both lines are perpendicular given that the measure of one of the angle is 90
d) This is incorrect
if angle 1 and angle 6 add up to 90 degrees, then angle 2 would be 90 degrees( this in observation of the rule that all the angles on a straight line add up to 180). So what this mean is that lines n and p and not r and p are perpendicular
e) This is incorrect
If the addition of both equals 90, then angle 5 is 90 according to the straight line addition equalling 180.
So if angle 5 is 90, then it is n and p that are perpendicular
f) This is correct
If both add up to be 90, then we can make a conclusion as both angles are directly between the lines r and p