SOLUTION: Given: CE bisects angle DCF measure of angle DCE = 2x+3y measure of ECF = 3x-y+2 measure of DCF = 80 find x and y

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Question 712254: Given: CE bisects angle DCF
measure of angle DCE = 2x+3y
measure of ECF = 3x-y+2
measure of DCF = 80
find x and y
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Those facts mean that 80 degrees is the sum of the measures of both angles, and the two angles resulting from the bisection are equal sizes.

80=%282x%2B3y%29%2B%283x-y%2B2%29 and 2x%2B3y=3x-y%2B2, two equations and two variables.

Work on each to change into standard form, Ax+By=C and then use substitution or elimination to solve for x and y.

The "80" equation:
2x%2B3x%2B3y-y%2B2=80
5x%2B2y=80-2
highlight%285x%2B2y=78%29, Use this equation in your system to solve.

The two equal angles equation:
2x-3x%2B3y%2By=2
-x%2B4y=2
highlight%28x-4y=-2%29, And use this equation in your system to solve.

You can finish the work.