SOLUTION: Line AE intersects line CD at point B, angle ABC = (x-2)(2x+2) and angle DBE = (x-1)(x+4). What is the measure of angle CBE?

Question 1084734: Line AE intersects line CD at point B, angle ABC = (x-2)(2x+2) and angle DBE = (x-1)(x+4). What is the measure of angle CBE?
Found 2 solutions by Qodiriy, mananth:
Answer by Qodiriy(1) (Show Source): You can put this solution on YOUR website!
If one line intersects the other, they together form four angles. They are called in my math study verticals and neighbour angles. Two vertical angles are equal and the sum of two other neighbour angles is 180�. I guess, there is no need to draw a picture. An angle ABC and an angle DBE are verticals thus they are equal.
(X-2)(2x+2)=(x-1)(x+4)
2x*x-4x+2x-4=x*x-x+4x-4
x*x-5x=0
x=5�. So
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!

(x-2)(2x+2) = (x-1)(x+4) (vertically opposite angles)
2x^2+2x-4x-4 = x^2+4x-x-4
x^2 -5x=0
x(x-5)=0
x= 0 or x=5
x not = 0
x=5
Plug value of x
(x-1)(x+4)
angle =36
angle CBE = 180-36 =144 ( supplementary angle)
.

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