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QuestionSolve for xx if angle LKM=7x−8LKM=7x-8 and angle NKM=x+1NKM=x+1, with KN bisecting angle LKM. What are xx and angle LKMLKM?

Studdy Solution

STEP 1

Assumptions1. KJ and KL are opposite rays. . KN bisects angle LKM.
3. Angle LKM =7x -8.
4. Angle NKM = x +1.

STEP 2

Since KN bisects angle LKM, we know that angle LKN = angle NKM.

STEP 3

We can set up the equation to represent this relationship.
Angle LKN=Angle NKMAngle\, LKN = Angle\, NKM

STEP 4

Substitute the given values for angle LKN and angle NKM into the equation.
7x−8=x+17x -8 = x +1

STEP 5

Subtract x from both sides of the equation to isolate the variable on one side.
7x−x=1+87x - x =1 +8

STEP 6

implify the equation to find the value of x.
6x=96x =9

STEP 7

Divide both sides of the equation by6 to solve for x.
x=96x = \frac{9}{6}

STEP 8

implify the fraction to get the value of x.
x=1.5x =1.5

STEP 9

Now that we have the value of x, we can substitute it into the equation for angle LKM to find its measure.
Angle LKM=7x−8Angle\, LKM =7x -8

STEP 10

Substitute the value of x into the equation.
Angle LKM=7(.5)−8Angle\, LKM =7(.5) -8

STEP 11

Calculate the measure of angle LKM.
Angle LKM=10.5−8=.5Angle\, LKM =10.5 -8 =.5So, x =.5 and Angle LKM =.5.

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