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QuestionSolve for xx and angle LKMLKM given that angle LKM=7x−8LKM = 7x - 8 and angle NKM=x+1NKM = x + 1.

Studdy Solution

STEP 1

Assumptions1. KJ and KL are opposite rays. . KN bisects angle LKM, which means it divides the angle into two equal parts.
3. The measure of angle LKM is given by the expression 7x−87x -8.
4. The measure of angle NKM is given by the expression x+1x +1.

STEP 2

Since KN bisects angle LKM, the measure of angle NKM is equal to the measure of angle LKN. Therefore, we can set up the equation7x−8=2(x+1)7x -8 =2(x +1)

STEP 3

Expand the right side of the equation7x−8=2x+27x -8 =2x +2

STEP 4

Subtract 2x2x from both sides of the equation to isolate the variable xx on one side7x−2x=2+87x -2x =2 +8

STEP 5

implify the equation5x=105x =10

STEP 6

Divide both sides of the equation by5 to solve for xxx=10/5x =10 /5

STEP 7

Calculate the value of xxx=2x =2

STEP 8

Now that we have the value of xx, we can substitute it into the expression for the measure of angle LKM to find its valueKM=7x−8KM =7x -8

STEP 9

Substitute x=2x =2 into the equationKM=7(2)−8KM =7(2) -8

STEP 10

Calculate the measure of angle LKMKM=14−8=6KM =14 -8 =6The solution is x=2x =2 and the measure of angle LKM is6 degrees.

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