Why does an angle that is supplementary to an acute angle have to be obtuse

This is because the total needs to be equal to 180 degrees. Since obtuse angles are greater than 90 degrees, then it needs an acute angle (lower than 90 degrees) to supplement it to equal 180

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c