Lines p and q intersect to form adjacent angles 1 and 2. If angle 1=8x+4 and angle 2=9x-4 find x so that p is perpendicular to q.

P and Q are perpendicular if the resulting angles are 90 degrees (or pi/2 radians). So by definition, we know that angle 1 = 90 and we also know that angle 2 = 90. Thus angle 1 = 90 = angle 2, so angle 1 = angle 2.

Basically, if we set them equal to each other then we can solve for x, and have the lines P and Q be perpendicular.

8x + 4 = 9x - 4

+ 4 = +4

8x + 8 = 9x

-8x = -8x

8 = x