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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.

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1 Answer

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