QuestionSolve for $x$ if $\angle NKL = 3x - 10$ and $\angle NKM = 2x + 20$ , with KN bisecting $\angle LKM$ .

Studdy Solution

STEP 1

Assumptions1. KJ and KL are opposite rays. . KN bisects angle LKM.
3. The measure of angle NKL is given by the expression $3x -10$ .
4. The measure of angle NKM is given by the expression $x +20$ .

STEP 2

Since KN bisects angle LKM, this means that angle NKL is equal to angle NKM. We can set up the equation $x -10 =2x +20$ .

STEP 3

To solve for $x$ , we can first subtract $2x$ from both sides of the equation to get $x -10 =20$ .

STEP 4

Next, add10 to both sides of the equation to isolate $x$ on one side. This gives us $x =30$ .

STEP 5

Now that we have the value of $x$ , we can substitute it into the expression for angle NKM to find its measure. The expression for angle NKM is $2x +20$ .

STEP 6

Substitute $x =30$ into the expression for angle NKM to get $2(30) +20$ .

STEP 7

Calculate the measure of angle NKM to get $60 +20 =80$ degrees.
The solution is $x =30$ and the measure of angle NKM is80 degrees.

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QuestionSolve for $x$ if $\angle NKL = 3x - 10$ and $\angle NKM = 2x + 20$ , with KN bisecting $\angle LKM$ .

Studdy Solution

STEP 1

Assumptions1. KJ and KL are opposite rays. . KN bisects angle LKM.
3. The measure of angle NKL is given by the expression $3x -10$ .
4. The measure of angle NKM is given by the expression $x +20$ .

STEP 2

Since KN bisects angle LKM, this means that angle NKL is equal to angle NKM. We can set up the equation $x -10 =2x +20$ .

STEP 3

To solve for $x$ , we can first subtract $2x$ from both sides of the equation to get $x -10 =20$ .

STEP 4

Next, add10 to both sides of the equation to isolate $x$ on one side. This gives us $x =30$ .

STEP 5

Now that we have the value of $x$ , we can substitute it into the expression for angle NKM to find its measure. The expression for angle NKM is $2x +20$ .

STEP 6

Substitute $x =30$ into the expression for angle NKM to get $2(30) +20$ .

STEP 7

Calculate the measure of angle NKM to get $60 +20 =80$ degrees.
The solution is $x =30$ and the measure of angle NKM is80 degrees.

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QuestionSolve for xxx if ∠NKL=3x−10\angle NKL = 3x - 10∠NKL=3x−10 and ∠NKM=2x+20\angle NKM = 2x + 20∠NKM=2x+20, with KN bisecting ∠LKM\angle LKM∠LKM.

Studdy Solution

STEP 1

Assumptions1. KJ and KL are opposite rays. . KN bisects angle LKM.3. The measure of angle NKL is given by the expression 3x−103x -103x−10.4. The measure of angle NKM is given by the expression x+20x +20x+20.

STEP 2

Since KN bisects angle LKM, this means that angle NKL is equal to angle NKM. We can set up the equation x−10=2x+20x -10 =2x +20x−10=2x+20.

STEP 3

To solve for xxx, we can first subtract 2x2x2x from both sides of the equation to get x−10=20x -10 =20x−10=20.

STEP 4

Next, add10 to both sides of the equation to isolate xxx on one side. This gives us x=30x =30x=30.

STEP 5

Now that we have the value of xxx, we can substitute it into the expression for angle NKM to find its measure. The expression for angle NKM is 2x+202x +202x+20.

STEP 6

Substitute x=30x =30x=30 into the expression for angle NKM to get 2(30)+202(30) +202(30)+20.

STEP 7

Calculate the measure of angle NKM to get 60+20=8060 +20 =8060+20=80 degrees.The solution is x=30x =30x=30 and the measure of angle NKM is80 degrees.

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QuestionSolve for $x$ if $\angle NKL = 3x - 10$ and $\angle NKM = 2x + 20$ , with KN bisecting $\angle LKM$ .

Assumptions1. KJ and KL are opposite rays. . KN bisects angle LKM.
3. The measure of angle NKL is given by the expression $3x -10$ .
4. The measure of angle NKM is given by the expression $x +20$ .

Since KN bisects angle LKM, this means that angle NKL is equal to angle NKM. We can set up the equation $x -10 =2x +20$ .

To solve for $x$ , we can first subtract $2x$ from both sides of the equation to get $x -10 =20$ .

Next, add10 to both sides of the equation to isolate $x$ on one side. This gives us $x =30$ .

Now that we have the value of $x$ , we can substitute it into the expression for angle NKM to find its measure. The expression for angle NKM is $2x +20$ .

Substitute $x =30$ into the expression for angle NKM to get $2(30) +20$ .

Calculate the measure of angle NKM to get $60 +20 =80$ degrees.
The solution is $x =30$ and the measure of angle NKM is80 degrees.